Pub Date : 2026-02-02DOI: 10.1016/j.jalgebra.2026.01.035
Raheleh Jafari , Francesco Strazzanti , Santiago Zarzuela Armengou
We describe the canonical module of a simplicial affine semigroup ring and its trace ideal. As a consequence, we characterize when is nearly Gorenstein in terms of arithmetic properties of the semigroup S. Then, we find some bounds for the Cohen-Macaulay type of when it is nearly Gorenstein. In particular, if it has codimension at most three, we prove that the Cohen-Macaulay type is at most three and this bound is sharp.
{"title":"On nearly Gorenstein affine semigroups","authors":"Raheleh Jafari , Francesco Strazzanti , Santiago Zarzuela Armengou","doi":"10.1016/j.jalgebra.2026.01.035","DOIUrl":"10.1016/j.jalgebra.2026.01.035","url":null,"abstract":"<div><div>We describe the canonical module of a simplicial affine semigroup ring <span><math><mi>K</mi><mo>[</mo><mi>S</mi><mo>]</mo></math></span> and its trace ideal. As a consequence, we characterize when <span><math><mi>K</mi><mo>[</mo><mi>S</mi><mo>]</mo></math></span> is nearly Gorenstein in terms of arithmetic properties of the semigroup <em>S</em>. Then, we find some bounds for the Cohen-Macaulay type of <span><math><mi>K</mi><mo>[</mo><mi>S</mi><mo>]</mo></math></span> when it is nearly Gorenstein. In particular, if it has codimension at most three, we prove that the Cohen-Macaulay type is at most three and this bound is sharp.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"694 ","pages":"Pages 676-702"},"PeriodicalIF":0.8,"publicationDate":"2026-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146172052","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 : 2026-01-30DOI: 10.1016/j.jalgebra.2026.01.032
Yajun Ma , Junling Zheng , Yu-Zhe Liu
In this paper, we investigate the behavior of Igusa-Todorov distances, extension and Rouquier dimensions under cleft extensions of abelian categories. We apply our results to Morita context rings, trivial extension rings, tensor rings and arrow removals.
{"title":"Three homological invariants under cleft extensions","authors":"Yajun Ma , Junling Zheng , Yu-Zhe Liu","doi":"10.1016/j.jalgebra.2026.01.032","DOIUrl":"10.1016/j.jalgebra.2026.01.032","url":null,"abstract":"<div><div>In this paper, we investigate the behavior of Igusa-Todorov distances, extension and Rouquier dimensions under cleft extensions of abelian categories. We apply our results to Morita context rings, trivial extension rings, tensor rings and arrow removals.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"694 ","pages":"Pages 287-323"},"PeriodicalIF":0.8,"publicationDate":"2026-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146172099","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 : 2026-01-29DOI: 10.1016/j.jalgebra.2025.12.034
André Carvalho , Pedro V. Silva
We prove that a subset of a virtually free group is rational if and only if the language of geodesic words representing its elements (in any generating set) is rational and that the language of geodesics representing conjugates of elements in a rational subset of a virtually free group is context-free. As a corollary, the doubly generalized conjugacy problem is decidable for rational subsets of finitely generated virtually free groups: there is an algorithm taking as input two rational subsets and of a virtually free group that decides whether there is one element of conjugate to an element of . For free groups, we prove that the same problem is decidable with rational constraints on the set of conjugators.
{"title":"Geodesic languages for rational subsets and conjugates in virtually free groups","authors":"André Carvalho , Pedro V. Silva","doi":"10.1016/j.jalgebra.2025.12.034","DOIUrl":"10.1016/j.jalgebra.2025.12.034","url":null,"abstract":"<div><div>We prove that a subset of a virtually free group is rational if and only if the language of geodesic words representing its elements (in any generating set) is rational and that the language of geodesics representing conjugates of elements in a rational subset of a virtually free group is context-free. As a corollary, the doubly generalized conjugacy problem is decidable for rational subsets of finitely generated virtually free groups: there is an algorithm taking as input two rational subsets <span><math><msub><mrow><mi>K</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> and <span><math><msub><mrow><mi>K</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> of a virtually free group that decides whether there is one element of <span><math><msub><mrow><mi>K</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> conjugate to an element of <span><math><msub><mrow><mi>K</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>. For free groups, we prove that the same problem is decidable with rational constraints on the set of conjugators.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"694 ","pages":"Pages 263-286"},"PeriodicalIF":0.8,"publicationDate":"2026-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146171956","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 : 2026-01-29DOI: 10.1016/j.jalgebra.2025.12.033
Rabeya Basu, Maria Ann Mathew
Let R be a regular ring of dimension d and L be a c-divisible monoid. If is trivial and , then we prove that the symplectic group is generated by elementary symplectic matrices over . When or R is a geometrically regular ring containing a field, then improved bounds have been established. We also discuss the linear case, extending the work of [14].
{"title":"K1-Stability of symplectic modules over monoid algebras","authors":"Rabeya Basu, Maria Ann Mathew","doi":"10.1016/j.jalgebra.2025.12.033","DOIUrl":"10.1016/j.jalgebra.2025.12.033","url":null,"abstract":"<div><div>Let <em>R</em> be a regular ring of dimension <em>d</em> and <em>L</em> be a <em>c</em>-divisible monoid. If <span><math><msub><mrow><mi>K</mi></mrow><mrow><mn>1</mn></mrow></msub><mrow><mi>Sp</mi></mrow><mo>(</mo><mi>R</mi><mo>)</mo></math></span> is trivial and <span><math><mi>k</mi><mo>≥</mo><mi>d</mi><mo>+</mo><mn>2</mn></math></span>, then we prove that the symplectic group <span><math><msub><mrow><mi>Sp</mi></mrow><mrow><mn>2</mn><mi>k</mi></mrow></msub><mo>(</mo><mi>R</mi><mo>[</mo><mi>L</mi><mo>]</mo><mo>)</mo></math></span> is generated by elementary symplectic matrices over <span><math><mi>R</mi><mo>[</mo><mi>L</mi><mo>]</mo></math></span>. When <span><math><mi>d</mi><mo>≤</mo><mn>1</mn></math></span> or <em>R</em> is a geometrically regular ring containing a field, then improved bounds have been established. We also discuss the linear case, extending the work of <span><span>[14]</span></span>.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"694 ","pages":"Pages 185-208"},"PeriodicalIF":0.8,"publicationDate":"2026-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146172049","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 : 2026-01-29DOI: 10.1016/j.jalgebra.2026.01.025
Cătălin Ciupercă
If δ is a derivation on a commutative noetherian ring A containing a field of characteristic zero and k is a positive integer, we study the ideals I of A satisfying . Most results are concerned with the behavior of their integral closures, rational powers, and arbitrary saturations.
{"title":"Ideals invariant under powers of derivations","authors":"Cătălin Ciupercă","doi":"10.1016/j.jalgebra.2026.01.025","DOIUrl":"10.1016/j.jalgebra.2026.01.025","url":null,"abstract":"<div><div>If <em>δ</em> is a derivation on a commutative noetherian ring <em>A</em> containing a field of characteristic zero and <em>k</em> is a positive integer, we study the ideals <em>I</em> of <em>A</em> satisfying <span><math><mi>δ</mi><msup><mrow><mo>(</mo><mi>I</mi><mo>)</mo></mrow><mrow><mi>k</mi></mrow></msup><mo>⊆</mo><mi>I</mi></math></span>. Most results are concerned with the behavior of their integral closures, rational powers, and arbitrary saturations.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"694 ","pages":"Pages 29-43"},"PeriodicalIF":0.8,"publicationDate":"2026-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146098442","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 : 2026-01-29DOI: 10.1016/j.jalgebra.2026.01.029
Maria-Grazia Ascenzi
Let D denote a rational curve of degree , with only ordinary singularities and spanning . We consider the normal bundle where φ denotes a generically one-to-one parametrization of D. We study the parameter that controls the splitting of in terms of line bundles. We find that specific properties of D, related to its singular points, characterize . These properties are: the multiplicities and the auxiliary curve associated to the largest multiplicity.
{"title":"The normal bundle of a rational curve is determined by specific properties of the curve's singularities","authors":"Maria-Grazia Ascenzi","doi":"10.1016/j.jalgebra.2026.01.029","DOIUrl":"10.1016/j.jalgebra.2026.01.029","url":null,"abstract":"<div><div>Let <em>D</em> denote a rational curve of degree <span><math><msub><mrow><mi>d</mi></mrow><mrow><mi>D</mi></mrow></msub><mo>≥</mo><mn>4</mn></math></span>, with only ordinary singularities and spanning <span><math><msup><mrow><mi>P</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span>. We consider the normal bundle <span><math><msub><mrow><mi>N</mi></mrow><mrow><mi>φ</mi></mrow></msub></math></span> where <em>φ</em> denotes a generically one-to-one parametrization of <em>D</em>. We study the parameter <span><math><msub><mrow><mi>d</mi></mrow><mrow><mn>0</mn><mi>D</mi></mrow></msub></math></span> that controls the splitting of <span><math><msub><mrow><mi>N</mi></mrow><mrow><mi>φ</mi></mrow></msub></math></span> in terms of line bundles. We find that specific properties of <em>D</em>, related to its singular points, characterize <span><math><msub><mrow><mi>d</mi></mrow><mrow><mn>0</mn><mi>D</mi></mrow></msub></math></span>. These properties are: the multiplicities and the auxiliary curve associated to the largest multiplicity.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"694 ","pages":"Pages 209-220"},"PeriodicalIF":0.8,"publicationDate":"2026-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146172050","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 : 2026-01-29DOI: 10.1016/j.jalgebra.2026.01.028
Yanbo Li , Xiangyu Qi , Kai Meng Tan
We classify the core blocks of Ariki-Koike algebras by their moving vectors. Using this classification, we obtain a necessary and sufficient condition for Scopes equivalence between two core blocks, and express the number of simple modules lying in a core block as a classical Kostka number. Under certain conditions on the multicharge and moving vector, we further relate the graded decomposition numbers of these blocks in characteristic zero to the graded decomposition numbers of the Iwahori-Hecke algebras of type A.
{"title":"Moving vectors and core blocks of Ariki-Koike algebras","authors":"Yanbo Li , Xiangyu Qi , Kai Meng Tan","doi":"10.1016/j.jalgebra.2026.01.028","DOIUrl":"10.1016/j.jalgebra.2026.01.028","url":null,"abstract":"<div><div>We classify the core blocks of Ariki-Koike algebras by their moving vectors. Using this classification, we obtain a necessary and sufficient condition for Scopes equivalence between two core blocks, and express the number of simple modules lying in a core block as a classical Kostka number. Under certain conditions on the multicharge and moving vector, we further relate the graded decomposition numbers of these blocks in characteristic zero to the graded decomposition numbers of the Iwahori-Hecke algebras of type <em>A</em>.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"694 ","pages":"Pages 497-563"},"PeriodicalIF":0.8,"publicationDate":"2026-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146172098","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 : 2026-01-29DOI: 10.1016/j.jalgebra.2026.01.024
Marco Boggi
The Lannes-Quillen theorem relates the mod-p cohomology of a finite group G with the mod-p cohomology of centralizers of abelian elementary p-subgroups of G, for a prime number. This theorem was extended to profinite groups whose mod-p cohomology algebra is finitely generated by Henn. In a weaker form, the Lannes-Quillen theorem was then extended by Symonds to arbitrary profinite groups. Building on Symonds' result, we formulate and prove a full version of this theorem for all profinite groups. For this purpose, we develop a theory of products for families of discrete torsion modules, parameterized by a profinite space1, which is dual, in a very precise sense, to the theory of coproducts for families of profinite modules, parameterized by a profinite space, developed by Haran, Melnikov and Ribes. In the last section, we give applications to the problem of conjugacy separability of p-torsion elements and finite p-subgroups.
{"title":"Lannes' T-functor and mod-p cohomology of profinite groups","authors":"Marco Boggi","doi":"10.1016/j.jalgebra.2026.01.024","DOIUrl":"10.1016/j.jalgebra.2026.01.024","url":null,"abstract":"<div><div>The Lannes-Quillen theorem relates the mod-<em>p</em> cohomology of a finite group <em>G</em> with the mod-<em>p</em> cohomology of centralizers of abelian elementary <em>p</em>-subgroups of <em>G</em>, for <span><math><mi>p</mi><mo>></mo><mn>0</mn></math></span> a prime number. This theorem was extended to profinite groups whose mod-<em>p</em> cohomology algebra is finitely generated by Henn. In a weaker form, the Lannes-Quillen theorem was then extended by Symonds to arbitrary profinite groups. Building on Symonds' result, we formulate and prove a full version of this theorem for all profinite groups. For this purpose, we develop a theory of products for families of discrete torsion modules, parameterized by a profinite space<span><span><sup>1</sup></span></span>, which is dual, in a very precise sense, to the theory of coproducts for families of profinite modules, parameterized by a profinite space, developed by Haran, Melnikov and Ribes. In the last section, we give applications to the problem of conjugacy separability of <em>p</em>-torsion elements and finite <em>p</em>-subgroups.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"694 ","pages":"Pages 109-147"},"PeriodicalIF":0.8,"publicationDate":"2026-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146172045","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 : 2026-01-29DOI: 10.1016/j.jalgebra.2026.01.026
Tuan Ngo Dac , Gia Vuong Nguyen Chu , Lan Huong Pham
In this paper we construct a polynomial basis for the stuffle algebra over a field of characteristic . As an application we derive the transcendence degree for multiple zeta values in positive characteristic of small weights. To our knowledge, the only known result is the case of weight 2 which was proved by Mishiba using a completely different approach.
{"title":"A polynomial basis for the stuffle algebra and its applications","authors":"Tuan Ngo Dac , Gia Vuong Nguyen Chu , Lan Huong Pham","doi":"10.1016/j.jalgebra.2026.01.026","DOIUrl":"10.1016/j.jalgebra.2026.01.026","url":null,"abstract":"<div><div>In this paper we construct a polynomial basis for the stuffle algebra over a field of characteristic <span><math><mi>p</mi><mo>></mo><mn>0</mn></math></span>. As an application we derive the transcendence degree for multiple zeta values in positive characteristic of small weights. To our knowledge, the only known result is the case of weight 2 which was proved by Mishiba using a completely different approach.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"694 ","pages":"Pages 221-244"},"PeriodicalIF":0.8,"publicationDate":"2026-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146172047","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 : 2026-01-29DOI: 10.1016/j.jalgebra.2026.01.023
Toshiyuki Tanisaki
We establish some properties of the ring of differential operators on the quantized flag manifold. Especially, we give an explicit description of its localization on an affine open subset in terms of the quantum Weyl algebra (q-analogue of boson).
{"title":"The ring of differential operators on a quantized flag manifold","authors":"Toshiyuki Tanisaki","doi":"10.1016/j.jalgebra.2026.01.023","DOIUrl":"10.1016/j.jalgebra.2026.01.023","url":null,"abstract":"<div><div>We establish some properties of the ring of differential operators on the quantized flag manifold. Especially, we give an explicit description of its localization on an affine open subset in terms of the quantum Weyl algebra (<em>q</em>-analogue of boson).</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"694 ","pages":"Pages 1-28"},"PeriodicalIF":0.8,"publicationDate":"2026-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146098441","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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