Pub Date : 2026-05-15Epub Date: 2026-01-29DOI: 10.1016/j.jalgebra.2025.12.030
Naoki Endo
As part of stratification of Cohen-Macaulay rings, we introduce and develop the theory of Goto rings, generalizing the notion of almost Gorenstein rings originally defined by V. Barucci and R. Fröberg in 1997. What has dominated the series of researches on almost Gorenstein rings is the fact that the reduction numbers of extended canonical ideals are at most 2; we define Goto rings as Cohen-Macaulay rings admitting such extended canonical ideals. We provide a characterization of Goto rings in terms of the structure of Sally modules and determine the Hilbert functions of them. Various examples of Goto rings that come from numerical semigroups, idealizations, fiber products, and equimultiple Ulrich ideals are explored as well.
{"title":"Goto rings","authors":"Naoki Endo","doi":"10.1016/j.jalgebra.2025.12.030","DOIUrl":"10.1016/j.jalgebra.2025.12.030","url":null,"abstract":"<div><div>As part of stratification of Cohen-Macaulay rings, we introduce and develop the theory of Goto rings, generalizing the notion of almost Gorenstein rings originally defined by V. Barucci and R. Fröberg in 1997. What has dominated the series of researches on almost Gorenstein rings is the fact that the reduction numbers of extended canonical ideals are at most 2; we define Goto rings as Cohen-Macaulay rings admitting such extended canonical ideals. We provide a characterization of Goto rings in terms of the structure of Sally modules and determine the Hilbert functions of them. Various examples of Goto rings that come from numerical semigroups, idealizations, fiber products, and equimultiple Ulrich ideals are explored as well.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"694 ","pages":"Pages 44-108"},"PeriodicalIF":0.8,"publicationDate":"2026-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146098461","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 : 2026-05-15Epub Date: 2026-02-02DOI: 10.1016/j.jalgebra.2026.01.034
Ulrich Krähmer , Myriam Mahaman
This article considers cuspidal curves whose coordinate rings are numerical semigroup algebras. Using a general result about descent of Hopf algebroid structures, their rings of differential operators are shown to be cocommutative and conilpotent left Hopf algebroids. If the semigroups are symmetric so that the curves are Gorenstein, they are full Hopf algebroids (admit an antipode).
{"title":"The ring of differential operators on a monomial curve is a Hopf algebroid","authors":"Ulrich Krähmer , Myriam Mahaman","doi":"10.1016/j.jalgebra.2026.01.034","DOIUrl":"10.1016/j.jalgebra.2026.01.034","url":null,"abstract":"<div><div>This article considers cuspidal curves whose coordinate rings are numerical semigroup algebras. Using a general result about descent of Hopf algebroid structures, their rings of differential operators are shown to be cocommutative and conilpotent left Hopf algebroids. If the semigroups are symmetric so that the curves are Gorenstein, they are full Hopf algebroids (admit an antipode).</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"694 ","pages":"Pages 564-628"},"PeriodicalIF":0.8,"publicationDate":"2026-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146172055","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 : 2026-05-15Epub Date: 2026-02-02DOI: 10.1016/j.jalgebra.2026.01.031
Alexander Ushakov , Chloe Weiers
In this paper we study the complexity of solving orientable quadratic equations in wreath products of finitely generated abelian groups. We give a classification of cases (depending on genus and other characteristics of a given equation) when the problem is computationally hard or feasible.
{"title":"Orientable quadratic equations in wreath products of abelian groups","authors":"Alexander Ushakov , Chloe Weiers","doi":"10.1016/j.jalgebra.2026.01.031","DOIUrl":"10.1016/j.jalgebra.2026.01.031","url":null,"abstract":"<div><div>In this paper we study the complexity of solving orientable quadratic equations in wreath products <span><math><mi>A</mi><mo>≀</mo><mi>B</mi></math></span> of finitely generated abelian groups. We give a classification of cases (depending on genus and other characteristics of a given equation) when the problem is computationally hard or feasible.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"694 ","pages":"Pages 324-358"},"PeriodicalIF":0.8,"publicationDate":"2026-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146171945","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 : 2026-05-15Epub Date: 2026-02-04DOI: 10.1016/j.jalgebra.2026.02.001
Kristian Ranestad , Anna Seigal , Kexin Wang
The classical trisecant lemma says that a general chord of a non-degenerate space curve is not a trisecant; that is, the chord only meets the curve in two points. The generalized trisecant lemma extends the result to higher-dimensional varieties. It states that the linear space spanned by general points on a projective variety intersects the variety in exactly these points, provided the dimension of the linear space is smaller than the codimension of the variety and that the variety is irreducible, reduced, and non-degenerate. We prove a real analog of the generalized trisecant lemma, which takes the form of a trichotomy. Along the way, we characterize the possible numbers of real intersection points between a real projective variety and a complementary dimension real linear space. We show that any integer of correct parity between a minimum and a maximum number can be achieved. We then specialize to Segre-Veronese varieties, where our results apply to the identifiability of independent component analysis, tensor decomposition, and typical tensor ranks.
{"title":"A real generalized trisecant trichotomy","authors":"Kristian Ranestad , Anna Seigal , Kexin Wang","doi":"10.1016/j.jalgebra.2026.02.001","DOIUrl":"10.1016/j.jalgebra.2026.02.001","url":null,"abstract":"<div><div>The classical trisecant lemma says that a general chord of a non-degenerate space curve is not a trisecant; that is, the chord only meets the curve in two points. The generalized trisecant lemma extends the result to higher-dimensional varieties. It states that the linear space spanned by general points on a projective variety intersects the variety in exactly these points, provided the dimension of the linear space is smaller than the codimension of the variety and that the variety is irreducible, reduced, and non-degenerate. We prove a real analog of the generalized trisecant lemma, which takes the form of a trichotomy. Along the way, we characterize the possible numbers of real intersection points between a real projective variety and a complementary dimension real linear space. We show that any integer of correct parity between a minimum and a maximum number can be achieved. We then specialize to Segre-Veronese varieties, where our results apply to the identifiability of independent component analysis, tensor decomposition, and typical tensor ranks.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"694 ","pages":"Pages 703-729"},"PeriodicalIF":0.8,"publicationDate":"2026-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146172053","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 : 2026-05-15Epub 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":"2026-05-15","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 : 2026-05-01Epub Date: 2026-01-21DOI: 10.1016/j.jalgebra.2026.01.003
Jinjin Liang, Wen Chen, Erxiao Wang
We develop the basic and new tools for classifying non-side-to-side tilings of the sphere by congruent triangles. Then we prove that, if the triangle has any irrational angle in degree, such tilings are: a sequence of 1-parameter families of triangles each admitting many 2-layer earth map tilings with 2n() tiles, together with rotational modifications for even n; a 1-parameter family of triangles each admitting a unique tiling with 8 tiles; and a sporadic triangle admitting a unique tiling with 16 tiles. Then a scheme is outlined to classify the case with all angles being rational in degree, justified by some known and new examples.
{"title":"Non-side-to-side tilings of the sphere by congruent triangles with an irrational angle","authors":"Jinjin Liang, Wen Chen, Erxiao Wang","doi":"10.1016/j.jalgebra.2026.01.003","DOIUrl":"10.1016/j.jalgebra.2026.01.003","url":null,"abstract":"<div><div>We develop the basic and new tools for classifying non-side-to-side tilings of the sphere by congruent triangles. Then we prove that, if the triangle has any irrational angle in degree, such tilings are: a sequence of 1-parameter families of triangles each admitting many 2-layer earth map tilings with 2<em>n</em>(<span><math><mi>n</mi><mo>≥</mo><mn>3</mn></math></span>) tiles, together with rotational modifications for even <em>n</em>; a 1-parameter family of triangles each admitting a unique tiling with 8 tiles; and a sporadic triangle admitting a unique tiling with 16 tiles. Then a scheme is outlined to classify the case with all angles being rational in degree, justified by some known and new examples.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"693 ","pages":"Pages 587-610"},"PeriodicalIF":0.8,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146075490","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 : 2026-05-01Epub Date: 2026-01-27DOI: 10.1016/j.jalgebra.2026.01.022
Thu T.H. Quan, Hung P. Tong-Viet
In this paper, we investigate certain generalizations of Camina pairs. Let H be a nontrivial proper subgroup of a finite group G. We first show that every nontrivial irreducible complex character of H induces homogeneously to G if and only if for every , the element x is conjugate to xh for all . Furthermore we prove that if xh is conjugate to either x or for all and all , then the normal closure N of H in G also satisfies the same condition, and N is nilpotent. Finally, we determine the structure of H under the assumption that for every element of odd order, the coset xH consists entirely of elements of odd order.
{"title":"Some generalizations of Camina pairs and orders of elements in cosets","authors":"Thu T.H. Quan, Hung P. Tong-Viet","doi":"10.1016/j.jalgebra.2026.01.022","DOIUrl":"10.1016/j.jalgebra.2026.01.022","url":null,"abstract":"<div><div>In this paper, we investigate certain generalizations of Camina pairs. Let <em>H</em> be a nontrivial proper subgroup of a finite group <em>G</em>. We first show that every nontrivial irreducible complex character of <em>H</em> induces homogeneously to <em>G</em> if and only if for every <span><math><mi>x</mi><mo>∈</mo><mi>G</mi><mo>∖</mo><mi>H</mi></math></span>, the element <em>x</em> is conjugate to <em>xh</em> for all <span><math><mi>h</mi><mo>∈</mo><mi>H</mi></math></span>. Furthermore we prove that if <em>xh</em> is conjugate to either <em>x</em> or <span><math><msup><mrow><mi>x</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></math></span> for all <span><math><mi>h</mi><mo>∈</mo><mi>H</mi></math></span> and all <span><math><mi>x</mi><mo>∈</mo><mi>G</mi><mo>∖</mo><mi>H</mi></math></span>, then the normal closure <em>N</em> of <em>H</em> in <em>G</em> also satisfies the same condition, and <em>N</em> is nilpotent. Finally, we determine the structure of <em>H</em> under the assumption that for every element <span><math><mi>x</mi><mo>∈</mo><mi>G</mi><mo>∖</mo><mi>H</mi></math></span> of odd order, the coset <em>xH</em> consists entirely of elements of odd order.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"693 ","pages":"Pages 838-862"},"PeriodicalIF":0.8,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146170547","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 : 2026-05-01Epub Date: 2026-01-21DOI: 10.1016/j.jalgebra.2026.01.020
Sheela Devadas
The global analogue of a Henselian local ring is a Henselian pair: a ring A and an ideal I which satisfy a condition resembling Hensel's lemma regarding lifting coprime factorizations of polynomials over to factorizations over A. The geometric counterpart is the notion of a Henselian scheme, which is an analogue of a tubular neighborhood in algebraic geometry.
In this paper we revisit the foundations of the theory of Henselian schemes. The pathological behavior of quasi-coherent sheaves on Henselian schemes in characteristic 0 makes them poor models for an “algebraic tube” in characteristic 0. We show that such problems do not arise in positive characteristic, and establish good properties for analogues of smooth and étale maps in the general Henselian setting.
{"title":"Henselian schemes in positive characteristic","authors":"Sheela Devadas","doi":"10.1016/j.jalgebra.2026.01.020","DOIUrl":"10.1016/j.jalgebra.2026.01.020","url":null,"abstract":"<div><div>The global analogue of a Henselian local ring is a Henselian pair: a ring <em>A</em> and an ideal <em>I</em> which satisfy a condition resembling Hensel's lemma regarding lifting coprime factorizations of polynomials over <span><math><mi>A</mi><mo>/</mo><mi>I</mi></math></span> to factorizations over <em>A</em>. The geometric counterpart is the notion of a Henselian scheme, which is an analogue of a tubular neighborhood in algebraic geometry.</div><div>In this paper we revisit the foundations of the theory of Henselian schemes. The pathological behavior of quasi-coherent sheaves on Henselian schemes in characteristic 0 makes them poor models for an “algebraic tube” in characteristic 0. We show that such problems do not arise in positive characteristic, and establish good properties for analogues of smooth and étale maps in the general Henselian setting.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"693 ","pages":"Pages 531-586"},"PeriodicalIF":0.8,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146025646","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 : 2026-05-01Epub Date: 2026-01-16DOI: 10.1016/j.jalgebra.2026.01.004
Dave Benson , Srikanth B. Iyengar , Henning Krause , Julia Pevtsova
For a point in the spectrum of the cohomology ring of a finite group G over a field k, we calculate the spectrum for the subcategory of dualisable objects inside the tensor triangulated category of -local and -torsion objects in the (big) stable module category of the group algebra kG.
{"title":"The spectrum of local dualisable modular representations","authors":"Dave Benson , Srikanth B. Iyengar , Henning Krause , Julia Pevtsova","doi":"10.1016/j.jalgebra.2026.01.004","DOIUrl":"10.1016/j.jalgebra.2026.01.004","url":null,"abstract":"<div><div>For a point <span><math><mi>p</mi></math></span> in the spectrum of the cohomology ring of a finite group <em>G</em> over a field <em>k</em>, we calculate the spectrum for the subcategory of dualisable objects inside the tensor triangulated category of <span><math><mi>p</mi></math></span>-local and <span><math><mi>p</mi></math></span>-torsion objects in the (big) stable module category of the group algebra <em>kG</em>.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"693 ","pages":"Pages 78-97"},"PeriodicalIF":0.8,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146001823","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 : 2026-05-01Epub Date: 2026-01-16DOI: 10.1016/j.jalgebra.2026.01.016
Xiaojun Yan , Xiuwu Zhu
Let be an elliptic curve, K an imaginary quadratic field, and let be a prime that splits in K and at which E has good ordinary reduction. Assume that the residual Galois representation associated with is irreducible. In this paper, we establish new cases of the two-variable Iwasawa main conjecture for E over K. As applications, we obtain more general results on the p-converse theorem and the p-part of the Birch and Swinnerton-Dyer formula in rank at most one.
{"title":"Main conjectures for non-CM elliptic curves at good ordinary primes","authors":"Xiaojun Yan , Xiuwu Zhu","doi":"10.1016/j.jalgebra.2026.01.016","DOIUrl":"10.1016/j.jalgebra.2026.01.016","url":null,"abstract":"<div><div>Let <span><math><mi>E</mi><mo>/</mo><mi>Q</mi></math></span> be an elliptic curve, <em>K</em> an imaginary quadratic field, and let <span><math><mi>p</mi><mo>></mo><mn>2</mn></math></span> be a prime that splits in <em>K</em> and at which <em>E</em> has good ordinary reduction. Assume that the residual Galois representation associated with <span><math><mo>(</mo><mi>E</mi><mo>,</mo><mi>p</mi><mo>)</mo></math></span> is irreducible. In this paper, we establish new cases of the two-variable Iwasawa main conjecture for <em>E</em> over <em>K</em>. As applications, we obtain more general results on the <em>p</em>-converse theorem and the <em>p</em>-part of the Birch and Swinnerton-Dyer formula in rank at most one.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"693 ","pages":"Pages 372-402"},"PeriodicalIF":0.8,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146025656","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}
扫码关注我们
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号