Journal of Algebra最新文献

{"title":"On structural connections between sandpile monoids and weighted Leavitt path algebras","authors":"Roozbeh Hazrat ,&nbsp;Tran Giang Nam","doi":"10.1016/j.jalgebra.2025.04.034","DOIUrl":"10.1016/j.jalgebra.2025.04.034","url":null,"abstract":"<div><div>In this article, we establish the relations between a sandpile graph, its sandpile monoid and the weighted Leavitt path algebra associated with it. Namely, we show that the lattice of all idempotents of the sandpile monoid <span><math><mtext>SP</mtext><mo>(</mo><mi>E</mi><mo>)</mo></math></span> of a sandpile graph <em>E</em> is both isomorphic to the lattice of all nonempty saturated hereditary subsets of <em>E</em>, the lattice of all order-ideals of <span><math><mtext>SP</mtext><mo>(</mo><mi>E</mi><mo>)</mo></math></span> and the lattice of all ideals of the weighted Leavitt path algebra <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>(</mo><mi>E</mi><mo>,</mo><mi>ω</mi><mo>)</mo></math></span> generated by vertices. Also, we describe the sandpile group of a sandpile graph <em>E</em> via archimedean classes of <span><math><mtext>SP</mtext><mo>(</mo><mi>E</mi><mo>)</mo></math></span>, and prove that all maximal subgroups of <span><math><mtext>SP</mtext><mo>(</mo><mi>E</mi><mo>)</mo></math></span> are exactly the Grothendieck groups of these archimedean classes. Finally, we give the structure of the Leavitt path algebra <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>(</mo><mi>E</mi><mo>)</mo></math></span> of a sandpile graph <em>E</em> via a finite chain of graded ideals being invariant under every graded automorphism of <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>(</mo><mi>E</mi><mo>)</mo></math></span>, and completely describe the structure of <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>(</mo><mi>E</mi><mo>)</mo></math></span> such that the lattice of all idempotents of <span><math><mtext>SP</mtext><mo>(</mo><mi>E</mi><mo>)</mo></math></span> is a chain. Consequently, we completely describe the structure of the weighted Leavitt path algebra of a sandpile graph <em>E</em> such that <span><math><mtext>SP</mtext><mo>(</mo><mi>E</mi><mo>)</mo></math></span> has exactly two idempotents.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"678 ","pages":"Pages 543-569"},"PeriodicalIF":0.8,"publicationDate":"2025-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143917760","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}

{"title":"Invariant theory of the queer color group","authors":"Tinu Dhali,&nbsp;Santosha Pattanayak,&nbsp;Preena Samuel","doi":"10.1016/j.jalgebra.2025.04.031","DOIUrl":"10.1016/j.jalgebra.2025.04.031","url":null,"abstract":"<div><div>In this paper, we introduce the notion of the queer color group, analogous to that of the queer supergroup over the infinite Grassmann algebra. We obtain a Schur-Weyl duality theorem for this group and thereby construct an explicit spanning set of invariants of the associated symmetric algebra of the mixed tensor space of a <em>G</em>-graded vector space where <em>G</em> is a finite abelian group. As a consequence, we obtain a generating set for the polynomial invariants, under the simultaneous action of the queer color group on color analogues of several copies of matrices. We also introduce the notion of concomitants for the queer color group analogous to that of Procesi in <span><span>[16]</span></span> and obtain a generating set for the algebra of concomitants. These results generalize those of Berele in <span><span>[3]</span></span> to the color setting.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"678 ","pages":"Pages 706-728"},"PeriodicalIF":0.8,"publicationDate":"2025-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143934935","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}

{"title":"On the minimal parabolic induction","authors":"Xinyu Li","doi":"10.1016/j.jalgebra.2025.04.026","DOIUrl":"10.1016/j.jalgebra.2025.04.026","url":null,"abstract":"<div><div>Motivated by Beilinson–Bernstein's proof of the Jantzen conjectures <span><span>[4]</span></span>, we define the minimal parabolic induction functor for Kac–Moody algebras, and establish some basic properties.</div><div>As applications of the formal theory, we examine first extension groups between simple highest weight modules in the category of weight modules, and analyze the annihilators of some simple highest weight modules.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"677 ","pages":"Pages 585-617"},"PeriodicalIF":0.8,"publicationDate":"2025-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143903505","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}

{"title":"Varieties of MV-monoids and positive MV-algebras","authors":"Marco Abbadini ,&nbsp;Paolo Aglianò ,&nbsp;Stefano Fioravanti","doi":"10.1016/j.jalgebra.2025.04.027","DOIUrl":"10.1016/j.jalgebra.2025.04.027","url":null,"abstract":"<div><div>MV-monoids are algebras <span><math><mo>〈</mo><mi>A</mi><mo>,</mo><mo>∨</mo><mo>,</mo><mo>∧</mo><mo>,</mo><mo>⊕</mo><mo>,</mo><mo>⊙</mo><mo>,</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>〉</mo></math></span> where <span><math><mo>〈</mo><mi>A</mi><mo>,</mo><mo>∨</mo><mo>,</mo><mo>∧</mo><mo>,</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>〉</mo></math></span> is a bounded distributive lattice, both <span><math><mo>〈</mo><mi>A</mi><mo>,</mo><mo>⊕</mo><mo>,</mo><mn>0</mn><mo>〉</mo></math></span> and <span><math><mo>〈</mo><mi>A</mi><mo>,</mo><mo>⊙</mo><mo>,</mo><mn>1</mn><mo>〉</mo></math></span> are commutative monoids, and some further connecting axioms are satisfied. Every MV-algebra in the signature <span><math><mo>{</mo><mo>⊕</mo><mo>,</mo><mo>¬</mo><mo>,</mo><mn>0</mn><mo>}</mo></math></span> is term equivalent to an algebra that has an MV-monoid as a reduct, by defining, as standard, <span><math><mn>1</mn><mo>≔</mo><mo>¬</mo><mn>0</mn></math></span>, <span><math><mi>x</mi><mo>⊙</mo><mi>y</mi><mo>≔</mo><mo>¬</mo><mo>(</mo><mo>¬</mo><mi>x</mi><mo>⊕</mo><mo>¬</mo><mi>y</mi><mo>)</mo></math></span>, <span><math><mi>x</mi><mo>∨</mo><mi>y</mi><mo>≔</mo><mo>(</mo><mi>x</mi><mo>⊙</mo><mo>¬</mo><mi>y</mi><mo>)</mo><mo>⊕</mo><mi>y</mi></math></span> and <span><math><mi>x</mi><mo>∧</mo><mi>y</mi><mo>≔</mo><mo>¬</mo><mo>(</mo><mo>¬</mo><mi>x</mi><mo>∨</mo><mo>¬</mo><mi>y</mi><mo>)</mo></math></span>. Particular examples of MV-monoids are positive MV-algebras, i.e., the <span><math><mo>{</mo><mo>∨</mo><mo>,</mo><mo>∧</mo><mo>,</mo><mo>⊕</mo><mo>,</mo><mo>⊙</mo><mo>,</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></span>-subreducts of MV-algebras. Positive MV-algebras form a peculiar quasivariety in the sense that, albeit having a logical motivation (being the quasivariety of subreducts of MV-algebras), it is not the equivalent quasivariety semantics of any logic.</div><div>In this paper, we study the lattices of subvarieties of MV-monoids and of positive MV-algebras. In particular, we characterize and axiomatize all almost minimal varieties of MV-monoids, we characterize the finite subdirectly irreducible positive MV-algebras, and we characterize and axiomatize all varieties of positive MV-algebras.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"677 ","pages":"Pages 690-744"},"PeriodicalIF":0.8,"publicationDate":"2025-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143922297","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}

{"title":"Corrigendum to “A note on the hit problem for the polynomial algebra of six variables and the sixth algebraic transfer” [J. Algebra 613 (2023) 1–31]","authors":"Đặng Võ Phúc","doi":"10.1016/j.jalgebra.2025.04.010","DOIUrl":"10.1016/j.jalgebra.2025.04.010","url":null,"abstract":"<div><div>In this corrigendum, we are making a slight correction to Remark 3.15 on pages 14–15 of <span><span>[1]</span></span>.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"678 ","pages":"Pages 463-464"},"PeriodicalIF":0.8,"publicationDate":"2025-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143895761","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}

{"title":"The finite groups with three automorphism orbits","authors":"Cai Heng Li,&nbsp;Yan Zhou Zhu","doi":"10.1016/j.jalgebra.2025.04.028","DOIUrl":"10.1016/j.jalgebra.2025.04.028","url":null,"abstract":"<div><div>A complete classification is given of finite groups whose elements are partitioned into three orbits by the automorphism groups, solving the long-standing classification problem initiated by G. Higman in 1963. As a consequence, a classification is obtained for finite permutation groups of rank 3 which are holomorphs of groups.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"678 ","pages":"Pages 677-705"},"PeriodicalIF":0.8,"publicationDate":"2025-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143934934","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}

{"title":"On cohomological characterizations of endotrivial modules","authors":"Fei Xu,&nbsp;Chenyou Zheng","doi":"10.1016/j.jalgebra.2025.04.021","DOIUrl":"10.1016/j.jalgebra.2025.04.021","url":null,"abstract":"<div><div>Given a general finite group <em>G</em>, there are various finite categories whose cohomology theories are of great interests. Recently Balmer and Grodal gave some new characterizations of the groups of endotrivial modules, via Čech cohomology and category cohomology, respectively, defined on certain orbit categories. These two seemingly different approaches share a common root in topos theory. We shall demonstrate the connection, which leads to a better understanding as well as new characterizations of the group of endotrivial modules.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"678 ","pages":"Pages 654-676"},"PeriodicalIF":0.8,"publicationDate":"2025-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143927826","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}

{"title":"General theory of localizations of rings and modules","authors":"V.V. Bavula","doi":"10.1016/j.jalgebra.2025.03.059","DOIUrl":"10.1016/j.jalgebra.2025.03.059","url":null,"abstract":"<div><div>The aim of the paper is to start to develop the most general theory of localizations/inversion. Several new concepts are introduced and studied.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"677 ","pages":"Pages 745-797"},"PeriodicalIF":0.8,"publicationDate":"2025-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143935178","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}

{"title":"Resolving the module of derivations on an n × (n + 1) determinantal ring","authors":"Henry Potts-Rubin","doi":"10.1016/j.jalgebra.2025.04.022","DOIUrl":"10.1016/j.jalgebra.2025.04.022","url":null,"abstract":"<div><div>We use the construction of the relative bar resolution via differential graded structures to obtain the minimal graded free resolution of <span><math><msub><mrow><mi>Der</mi></mrow><mrow><mi>R</mi><mo>|</mo><mi>k</mi></mrow></msub></math></span>, where <em>R</em> is a determinantal ring defined by the maximal minors of an <span><math><mi>n</mi><mo>×</mo><mo>(</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo></math></span> generic matrix and <em>k</em> is its coefficient field. Along the way, we compute an explicit action of the Hilbert-Burch differential graded algebra on a differential graded module resolving the cokernel of the Jacobian matrix whose kernel is <span><math><msub><mrow><mi>Der</mi></mrow><mrow><mi>R</mi><mo>|</mo><mi>k</mi></mrow></msub></math></span>. As a consequence of the minimality of the resulting relative bar resolution, we get a minimal generating set for <span><math><msub><mrow><mi>Der</mi></mrow><mrow><mi>R</mi><mo>|</mo><mi>k</mi></mrow></msub></math></span> as an <em>R</em>-module, which, while already known, has not been obtained via our methods.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"678 ","pages":"Pages 601-634"},"PeriodicalIF":0.8,"publicationDate":"2025-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143917762","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}

{"title":"On sequentially Cohen-Macaulay modules and sequentially generalized Cohen-Macaulay modules","authors":"Nguyen Xuan Linh ,&nbsp;Le Thanh Nhan","doi":"10.1016/j.jalgebra.2025.04.024","DOIUrl":"10.1016/j.jalgebra.2025.04.024","url":null,"abstract":"<div><div>We introduce the notions of <em>sequential sequence</em> and <em>sequential f-sequence</em> in order to characterize sequentially Cohen-Macaulay modules and sequentially generalized Cohen-Macaulay modules. Let <em>R</em> be a Noetherian local ring and <em>M</em> a finitely generated <em>R</em>-module. We show that <em>M</em> is sequentially Cohen-Macaulay (resp. sequentially generalized Cohen-Macaulay) if and only if there exists a system of parameters of <em>M</em> that is an <em>M</em>-sequential sequence (resp. each generalized regular sequence s.o.p of <em>M</em> is an <em>M</em>-sequential f-sequence) and <span><math><mi>R</mi><mo>/</mo><msub><mrow><mi>Ann</mi></mrow><mrow><mi>R</mi></mrow></msub><mo>(</mo><mi>M</mi><mo>)</mo></math></span> is a quotient of a Cohen-Macaulay local ring. As an application, we give new characterizations of Cohen-Macaulay modules and generalized Cohen-Macaulay modules.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"678 ","pages":"Pages 635-653"},"PeriodicalIF":0.8,"publicationDate":"2025-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143927836","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}