Pub Date : 2026-01-20DOI: 10.1016/j.jalgebra.2026.01.019
Tommy Hofmann
We consider the computational problem of determining the unit group of a finite ring, by which we mean the computation of a finite presentation together with an algorithm to express units as words in the generators. We show that the problem is equivalent to the number theoretic problems of factoring integers and solving discrete logarithms in finite fields. A similar equivalence is shown for the problem of determining the abelianization of the unit group or the first K-group of finite rings.
{"title":"Determining unit groups and K1 of finite rings","authors":"Tommy Hofmann","doi":"10.1016/j.jalgebra.2026.01.019","DOIUrl":"10.1016/j.jalgebra.2026.01.019","url":null,"abstract":"<div><div>We consider the computational problem of determining the unit group of a finite ring, by which we mean the computation of a finite presentation together with an algorithm to express units as words in the generators. We show that the problem is equivalent to the number theoretic problems of factoring integers and solving discrete logarithms in finite fields. A similar equivalence is shown for the problem of determining the abelianization of the unit group or the first <em>K</em>-group of finite rings.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"693 ","pages":"Pages 510-530"},"PeriodicalIF":0.8,"publicationDate":"2026-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146025708","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-19DOI: 10.1016/j.jalgebra.2026.01.008
Elshani Kamberi, Francesco Navarra, Ayesha Asloob Qureshi
In this article, we study the squarefree powers of facet ideals associated with simplicial trees. Specifically, we examine the linearity of their minimal free resolution and their regularity. Additionally, we investigate when the first syzygy module of squarefree powers of facet ideal of a simplicial tree is generated by linear relations. Finally, we provide a combinatorial formula for the regularity of the squarefree powers of t-path ideals of path graphs.
{"title":"On squarefree powers of simplicial trees","authors":"Elshani Kamberi, Francesco Navarra, Ayesha Asloob Qureshi","doi":"10.1016/j.jalgebra.2026.01.008","DOIUrl":"10.1016/j.jalgebra.2026.01.008","url":null,"abstract":"<div><div>In this article, we study the squarefree powers of facet ideals associated with simplicial trees. Specifically, we examine the linearity of their minimal free resolution and their regularity. Additionally, we investigate when the first syzygy module of squarefree powers of facet ideal of a simplicial tree is generated by linear relations. Finally, we provide a combinatorial formula for the regularity of the squarefree powers of <em>t</em>-path ideals of path graphs.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"693 ","pages":"Pages 240-276"},"PeriodicalIF":0.8,"publicationDate":"2026-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146025652","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-19DOI: 10.1016/j.jalgebra.2026.01.010
Ryo Ishizuka , Kei Nakazato
In this paper, we prove “prismatic Kunz's theorem” which states that a complete Noetherian local ring R of residue characteristic p is a regular local ring if and only if the Frobenius lift on a prismatic complex of (a derived enhancement of) R over a specific prism is faithfully flat. This generalizes classical Kunz's theorem from the perspective of extending the “Frobenius map” to mixed characteristic rings. Our approach involves studying the deformation problem of the “regularity” of prisms and demonstrating the faithful flatness of the structure map of the prismatic complex.
{"title":"Prismatic Kunz's theorem","authors":"Ryo Ishizuka , Kei Nakazato","doi":"10.1016/j.jalgebra.2026.01.010","DOIUrl":"10.1016/j.jalgebra.2026.01.010","url":null,"abstract":"<div><div>In this paper, we prove “prismatic Kunz's theorem” which states that a complete Noetherian local ring <em>R</em> of residue characteristic <em>p</em> is a regular local ring if and only if the Frobenius lift on a prismatic complex of (a derived enhancement of) <em>R</em> over a specific prism <span><math><mo>(</mo><mi>A</mi><mo>,</mo><mi>I</mi><mo>)</mo></math></span> is faithfully flat. This generalizes classical Kunz's theorem from the perspective of extending the “Frobenius map” to mixed characteristic rings. Our approach involves studying the deformation problem of the “regularity” of prisms and demonstrating the faithful flatness of the structure map of the prismatic complex.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"693 ","pages":"Pages 732-769"},"PeriodicalIF":0.8,"publicationDate":"2026-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146075494","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-19DOI: 10.1016/j.jalgebra.2026.01.013
Takuma Hayashi
In this paper, we establish general categorical frameworks that extend Loewy's classification scheme for finite-dimensional real irreducible representations of groups and Borel–Tits' criterion for the existence of rational forms of representations of for a connected reductive algebraic group G over a field F of characteristic zero and its algebraic closure . We also discuss applications of these general formalisms to the theory of Harish-Chandra modules, specifically to classify irreducible Harish-Chandra modules over fields F of characteristic zero and to identify smaller fields of definition of irreducible Harish-Chandra modules over , particularly in the case of cohomological irreducible essentially unitarizable modules.
{"title":"Rationality patterns","authors":"Takuma Hayashi","doi":"10.1016/j.jalgebra.2026.01.013","DOIUrl":"10.1016/j.jalgebra.2026.01.013","url":null,"abstract":"<div><div>In this paper, we establish general categorical frameworks that extend Loewy's classification scheme for finite-dimensional real irreducible representations of groups and Borel–Tits' criterion for the existence of rational forms of representations of <span><math><mover><mrow><mi>F</mi></mrow><mrow><mo>¯</mo></mrow></mover><msub><mrow><mo>⊗</mo></mrow><mrow><mi>F</mi></mrow></msub><mi>G</mi></math></span> for a connected reductive algebraic group <em>G</em> over a field <em>F</em> of characteristic zero and its algebraic closure <span><math><mover><mrow><mi>F</mi></mrow><mrow><mo>¯</mo></mrow></mover></math></span>. We also discuss applications of these general formalisms to the theory of Harish-Chandra modules, specifically to classify irreducible Harish-Chandra modules over fields <em>F</em> of characteristic zero and to identify smaller fields of definition of irreducible Harish-Chandra modules over <span><math><mover><mrow><mi>F</mi></mrow><mrow><mo>¯</mo></mrow></mover></math></span>, particularly in the case of cohomological irreducible essentially unitarizable modules.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"693 ","pages":"Pages 157-212"},"PeriodicalIF":0.8,"publicationDate":"2026-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146025650","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-19DOI: 10.1016/j.jalgebra.2026.01.012
Mitra Koley , Arvind Kumar
In this article, we extend the notion of F-thresholds of ideals to F-thresholds of filtrations of ideals. We establish the existence of F-thresholds for various types of filtrations, including symbolic power filtrations and integral closure filtrations. Additionally, we outline various necessary and sufficient conditions for the finiteness of F-thresholds. We also provide effective upper bounds for symbolic F-thresholds.
Furthermore, we provide a numerical criterion for the symbolic F-splitting, a recently defined F-singularity, in terms of its symbolic F-threshold. We initiate the study of F-thresholds through valuation theory and establish an upper bound in terms of valuations. We also present a formula for the F-threshold of any monomial ideal in terms of its Rees valuations. Lastly, we compute symbolic F-thresholds for various determinantal ideals, F-König ideals, and more.
{"title":"F-thresholds of filtrations of ideals","authors":"Mitra Koley , Arvind Kumar","doi":"10.1016/j.jalgebra.2026.01.012","DOIUrl":"10.1016/j.jalgebra.2026.01.012","url":null,"abstract":"<div><div>In this article, we extend the notion of <em>F</em>-thresholds of ideals to <em>F</em>-thresholds of filtrations of ideals. We establish the existence of <em>F</em>-thresholds for various types of filtrations, including symbolic power filtrations and integral closure filtrations. Additionally, we outline various necessary and sufficient conditions for the finiteness of <em>F</em>-thresholds. We also provide effective upper bounds for symbolic <em>F</em>-thresholds.</div><div>Furthermore, we provide a numerical criterion for the symbolic <em>F</em>-splitting, a recently defined <em>F</em>-singularity, in terms of its symbolic <em>F</em>-threshold. We initiate the study of <em>F</em>-thresholds through valuation theory and establish an upper bound in terms of valuations. We also present a formula for the <em>F</em>-threshold of any monomial ideal in terms of its Rees valuations. Lastly, we compute symbolic <em>F</em>-thresholds for various determinantal ideals, <em>F</em>-König ideals, and more.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"693 ","pages":"Pages 1-35"},"PeriodicalIF":0.8,"publicationDate":"2026-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146001819","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-19DOI: 10.1016/j.jalgebra.2025.12.027
Madeline Nurcombe
The ghost algebra is a two-boundary extension of the Temperley–Lieb algebra, constructed recently via a diagrammatic presentation. The existing two-boundary Temperley–Lieb algebra has a basis of two-boundary string diagrams, where the number of strings connected to each boundary must be even. The ghost algebra is similar, but allows this number to be odd, using bookkeeping dots called ghosts to assign a consistent parity to each string endpoint on each boundary. Equivalently, one can discard the ghosts and label each string endpoint with its parity; the resulting algebra is readily generalised to allow any number of possible labels, instead of just odd or even. We call the generalisation the label algebra, and establish a non-diagrammatic presentation for it. A similar presentation for the ghost algebra follows from this.
{"title":"Presentations for the ghost algebra and the label algebra","authors":"Madeline Nurcombe","doi":"10.1016/j.jalgebra.2025.12.027","DOIUrl":"10.1016/j.jalgebra.2025.12.027","url":null,"abstract":"<div><div>The ghost algebra is a two-boundary extension of the Temperley–Lieb algebra, constructed recently via a diagrammatic presentation. The existing two-boundary Temperley–Lieb algebra has a basis of two-boundary string diagrams, where the number of strings connected to each boundary must be even. The ghost algebra is similar, but allows this number to be odd, using bookkeeping dots called <em>ghosts</em> to assign a consistent parity to each string endpoint on each boundary. Equivalently, one can discard the ghosts and label each string endpoint with its parity; the resulting algebra is readily generalised to allow any number of possible labels, instead of just odd or even. We call the generalisation the <em>label algebra</em>, and establish a non-diagrammatic presentation for it. A similar presentation for the ghost algebra follows from this.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"693 ","pages":"Pages 611-682"},"PeriodicalIF":0.8,"publicationDate":"2026-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146075491","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-19DOI: 10.1016/j.jalgebra.2026.01.011
Shiro Goto , Shinya Kumashiro
In this paper, we introduce generalized Gorenstein local (GGL) rings. The notion of GGL rings is a natural generalization of the notion of almost Gorenstein rings, which can thus be treated as part of the theory of GGL rings. For a Cohen-Macaulay local ring R, we explore the endomorphism algebra of the maximal ideal, the trace ideal of the canonical module, Ulrich ideals, and Rees algebras of parameter ideals in connection with the GGL property. We also give numerous examples of numerical semigroup rings, idealizations, and determinantal rings of certain matrices.
{"title":"On generalized Gorenstein local rings","authors":"Shiro Goto , Shinya Kumashiro","doi":"10.1016/j.jalgebra.2026.01.011","DOIUrl":"10.1016/j.jalgebra.2026.01.011","url":null,"abstract":"<div><div>In this paper, we introduce generalized Gorenstein local (GGL) rings. The notion of GGL rings is a natural generalization of the notion of almost Gorenstein rings, which can thus be treated as part of the theory of GGL rings. For a Cohen-Macaulay local ring <em>R</em>, we explore the endomorphism algebra of the maximal ideal, the trace ideal of the canonical module, Ulrich ideals, and Rees algebras of parameter ideals in connection with the GGL property. We also give numerous examples of numerical semigroup rings, idealizations, and determinantal rings of certain matrices.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"693 ","pages":"Pages 98-156"},"PeriodicalIF":0.8,"publicationDate":"2026-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146025649","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-19DOI: 10.1016/j.jalgebra.2026.01.018
Tomasz Brzeziński , Krzysztof Radziszewski , Brais Ramos Pérez
A general procedure of affinization of linear algebra structures is illustrated by the case of Leibniz algebras. Specifically, the definition of an affine Leibniz bracket, that is, a bi-affine operation on an affine space that at each tangent vector space becomes a (bi-linear) Leibniz bracket in terms of a tri-affine operation called a Leibnizian, is given. An affine space together with such an operation is called a Leibniz affgebra. It is shown that any Leibniz algebra can be extended to a family of Leibniz affgebras. Depending on the choice of a Leibnizian different types of Leibniz affgebras are introduced. These include: derivative-type, which captures the derivation property of linear Leibniz bracket; homogeneous-type, which is based on the simplest and least restrictive choice of the Leibnizian; Lie-type which includes all Lie affgebras introduced in R.R. Andruszkiewicz, T. Brzeziński & K. Radziszewski (2025) [1]. Each type is illustrated by examples with prescribed Leibniz algebra fibres.
以莱布尼兹代数为例，说明了线性代数结构的一般仿射过程。具体地说，给出了仿射莱布尼茨括号的定义，即仿射空间上的双仿射操作，该操作在每个切向量空间上都成为一个（双线性）莱布尼茨括号，这是一个三仿射操作，称为莱布尼茨算子。一个仿射空间加上这样的运算称为莱布尼茨仿射。证明了任何莱布尼茨代数都可以推广到一类莱布尼茨共轭代数。根据对莱布尼茨元的选择，引入了不同类型的莱布尼茨仿形。它们包括：导数型，捕捉线性莱布尼茨括号的导数性质；齐次型，它是基于最简单和限制最小的莱布尼兹选择；Lie-type包括R.R. Andruszkiewicz， T. Brzeziński &； K. Radziszewski(2025)[1]。每种类型都用规定的莱布尼茨代数纤维举例说明。
{"title":"Affinization of algebraic structures: Leibniz algebras","authors":"Tomasz Brzeziński , Krzysztof Radziszewski , Brais Ramos Pérez","doi":"10.1016/j.jalgebra.2026.01.018","DOIUrl":"10.1016/j.jalgebra.2026.01.018","url":null,"abstract":"<div><div>A general procedure of affinization of linear algebra structures is illustrated by the case of Leibniz algebras. Specifically, the definition of an affine Leibniz bracket, that is, a bi-affine operation on an affine space that at each tangent vector space becomes a (bi-linear) Leibniz bracket in terms of a tri-affine operation called a Leibnizian, is given. An affine space together with such an operation is called a Leibniz affgebra. It is shown that any Leibniz algebra can be extended to a family of Leibniz affgebras. Depending on the choice of a Leibnizian different types of Leibniz affgebras are introduced. These include: derivative-type, which captures the derivation property of linear Leibniz bracket; homogeneous-type, which is based on the simplest and least restrictive choice of the Leibnizian; Lie-type which includes all Lie affgebras introduced in R.R. Andruszkiewicz, T. Brzeziński & K. Radziszewski (2025) <span><span>[1]</span></span>. Each type is illustrated by examples with prescribed Leibniz algebra fibres.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"693 ","pages":"Pages 329-361"},"PeriodicalIF":0.8,"publicationDate":"2026-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146025654","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-19DOI: 10.1016/j.jalgebra.2026.01.009
Yan Cao , Yuan Shen , Xin Wang
Let A be a Koszul Artin-Schelter regular algebra and be a graded double Ore extension of A where is a graded algebra homomorphism and is a degree one ς-derivation. We construct a minimal free resolution for the trivial module of B, and it implies that B is still Koszul. We introduce a homological invariant called ς-divergence of ν, and with its aid, we obtain a precise description of the Nakayama automorphism of B. A twisted superpotential for B with respect to the Nakayama automorphism is constructed so that B is isomorphic to the derivation quotient algebra of .
{"title":"Nakayama automorphisms of graded double Ore extensions of Koszul Artin-Schelter regular algebras with nontrivial skew derivations","authors":"Yan Cao , Yuan Shen , Xin Wang","doi":"10.1016/j.jalgebra.2026.01.009","DOIUrl":"10.1016/j.jalgebra.2026.01.009","url":null,"abstract":"<div><div>Let <em>A</em> be a Koszul Artin-Schelter regular algebra and <span><math><mi>B</mi><mo>=</mo><msub><mrow><mi>A</mi></mrow><mrow><mi>P</mi></mrow></msub><mo>[</mo><msub><mrow><mi>y</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>y</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>;</mo><mi>ς</mi><mo>,</mo><mi>ν</mi><mo>]</mo></math></span> be a graded double Ore extension of <em>A</em> where <span><math><mi>ς</mi><mo>:</mo><mi>A</mi><mo>→</mo><msub><mrow><mi>M</mi></mrow><mrow><mn>2</mn><mo>×</mo><mn>2</mn></mrow></msub><mo>(</mo><mi>A</mi><mo>)</mo></math></span> is a graded algebra homomorphism and <span><math><mi>ν</mi><mo>:</mo><mi>A</mi><mo>→</mo><msup><mrow><mi>A</mi></mrow><mrow><mo>⊕</mo><mn>2</mn></mrow></msup></math></span> is a degree one <em>ς</em>-derivation. We construct a minimal free resolution for the trivial module of <em>B</em>, and it implies that <em>B</em> is still Koszul. We introduce a homological invariant called <em>ς</em>-divergence of <em>ν</em>, and with its aid, we obtain a precise description of the Nakayama automorphism of <em>B</em>. A twisted superpotential <span><math><mover><mrow><mi>ω</mi></mrow><mrow><mo>ˆ</mo></mrow></mover></math></span> for <em>B</em> with respect to the Nakayama automorphism is constructed so that <em>B</em> is isomorphic to the derivation quotient algebra of <span><math><mover><mrow><mi>ω</mi></mrow><mrow><mo>ˆ</mo></mrow></mover></math></span>.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"693 ","pages":"Pages 403-449"},"PeriodicalIF":0.8,"publicationDate":"2026-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146025648","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-19DOI: 10.1016/j.jalgebra.2026.01.017
Yongle Luo , Baptiste Rognerud
For a finite lattice, we consider the lattice of all its weak factorization systems, or equivalently of all its transfer systems. We prove that it enjoys very strong properties such as semidistributivity, trimness and congruence uniformity. We introduce the elevating graph of a finite lattice as a particular graph whose vertices are the relations of the lattice and we prove that there is a bijection between the transfer systems and the cliques of this graph. This bijection provides a combinatorial model for the problem of enumerating the transfer systems. As illustrations, we recover a known result for the diamond lattices and we obtain a very large lower bound for the boolean lattices.
{"title":"On the lattice of the weak factorization systems on a finite lattice","authors":"Yongle Luo , Baptiste Rognerud","doi":"10.1016/j.jalgebra.2026.01.017","DOIUrl":"10.1016/j.jalgebra.2026.01.017","url":null,"abstract":"<div><div>For a finite lattice, we consider the lattice of all its weak factorization systems, or equivalently of all its transfer systems. We prove that it enjoys very strong properties such as semidistributivity, trimness and congruence uniformity. We introduce the elevating graph of a finite lattice as a particular graph whose vertices are the relations of the lattice and we prove that there is a bijection between the transfer systems and the cliques of this graph. This bijection provides a combinatorial model for the problem of enumerating the transfer systems. As illustrations, we recover a known result for the diamond lattices and we obtain a very large lower bound for the boolean lattices.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"693 ","pages":"Pages 277-328"},"PeriodicalIF":0.8,"publicationDate":"2026-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146025653","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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