Journal of Pure and Applied Algebra最新文献

{"title":"On the projective normality of Ulrich bundles on some low-dimensional varieties","authors":"Valerio Buttinelli","doi":"10.1016/j.jpaa.2026.108192","DOIUrl":"10.1016/j.jpaa.2026.108192","url":null,"abstract":"<div><div>We study the projective normality of the projective bundle of an Ulrich vector bundle embedded through the complete linear system of its tautological line bundle. The focus will be on Ulrich bundles defined over curves, surfaces with <span><math><mi>q</mi><mo>=</mo><msub><mrow><mi>p</mi></mrow><mrow><mi>g</mi></mrow></msub><mo>=</mo><mn>0</mn></math></span> and hypersurfaces of dimension 2 and 3.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"230 2","pages":"Article 108192"},"PeriodicalIF":0.8,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146174132","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":"Betti numbers for modules over Artinian local rings","authors":"Kaiyue He","doi":"10.1016/j.jpaa.2026.108172","DOIUrl":"10.1016/j.jpaa.2026.108172","url":null,"abstract":"<div><div>We introduce a new numerical invariant <span><math><msub><mrow><mi>γ</mi></mrow><mrow><mi>I</mi></mrow></msub><mo>(</mo><mi>M</mi><mo>)</mo></math></span> associated to a finite-length <em>R</em>-module <em>M</em> and an ideal <em>I</em> in an Artinian local ring <em>R</em>. This invariant measures the ratio between <span><math><mi>λ</mi><mo>(</mo><mi>I</mi><mi>M</mi><mo>)</mo></math></span> and <span><math><mi>λ</mi><mo>(</mo><mi>M</mi><mo>/</mo><mi>I</mi><mi>M</mi><mo>)</mo></math></span>. We establish fundamental relationships between this invariant and the Betti numbers of the module under the assumption of the Tor modules vanishing. In particular, we use this invariant to establish a freeness criterion for modules under certain Tor vanishing conditions. The criterion applies specifically to the class of <em>I</em>-free modules — those modules <em>M</em> for which <span><math><mi>M</mi><mo>/</mo><mi>I</mi><mi>M</mi></math></span> is isomorphic to a direct sum of copies of <span><math><mi>R</mi><mo>/</mo><mi>I</mi></math></span>. Lastly, we apply these results to the canonical module, proving that, under certain conditions on the ring structure, when the zeroth Betti number is greater than or equal to the first Betti number of the canonical module, then the ring is Gorenstein. This partially answers a question posed by Jorgensen and Leuschke concerning the relationship between Betti numbers of the canonical module and Gorenstein properties.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"230 2","pages":"Article 108172"},"PeriodicalIF":0.8,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145981621","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":"Profinite and solid cohomology","authors":"Jiacheng Tang","doi":"10.1016/j.jpaa.2026.108189","DOIUrl":"10.1016/j.jpaa.2026.108189","url":null,"abstract":"<div><div>Solid abelian groups, as introduced by Dustin Clausen and Peter Scholze, form a subcategory of all condensed abelian groups satisfying some “completeness” conditions and having favourable categorical properties. Given a profinite ring <em>R</em>, there is an associated condensed ring <span><math><munder><mrow><mi>R</mi></mrow><mo>_</mo></munder></math></span> which is solid. We show that the natural embedding of profinite <em>R</em>-modules into solid <span><math><munder><mrow><mi>R</mi></mrow><mo>_</mo></munder></math></span>-modules preserves Ext and tensor products, as well as the fact that profinite rings are analytic.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"230 2","pages":"Article 108189"},"PeriodicalIF":0.8,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146174131","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 connective Morava K-theory of the second mod p Eilenberg-MacLane space","authors":"Donald M. Davis ,&nbsp;Douglas C. Ravenel ,&nbsp;W. Stephen Wilson","doi":"10.1016/j.jpaa.2026.108171","DOIUrl":"10.1016/j.jpaa.2026.108171","url":null,"abstract":"<div><div>We develop tools for computing the connective n-th Morava K-theory of spaces. Starting with a Universal Coefficient Theorem that computes the cohomology version from the homology version, we show that every step in the process of computing one is mirrored in the other and that this can be used to make computations. As our example, we compute the connective <em>n</em>-th Morava <em>K</em>-theory of the second mod <em>p</em> Eilenberg-MacLane space.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"230 2","pages":"Article 108171"},"PeriodicalIF":0.8,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145981620","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":"Matrix Fejér-Riesz type theorem for a union of an interval and a point","authors":"Shengding Sun ,&nbsp;Aljaž Zalar","doi":"10.1016/j.jpaa.2026.108173","DOIUrl":"10.1016/j.jpaa.2026.108173","url":null,"abstract":"<div><div>The matrix Fejér-Riesz theorem characterizes positive semidefinite matrix polynomials on the real line. In <span><span>[28]</span></span> this was extended to the characterization on arbitrary closed semialgebraic sets <span><math><mi>K</mi><mo>⊆</mo><mi>R</mi></math></span> by using matrix quadratic modules from real algebraic geometry. In the compact case there is a denominator-free characterization, while in the non-compact case denominators are needed except when <em>K</em> is the whole line, an unbounded interval, a union of two unbounded intervals, and according to a conjecture of <span><span>[28]</span></span> also when <em>K</em> is a union of an unbounded interval and a point or a union of two unbounded intervals and a point. In this paper, we confirm this conjecture by solving the truncated matrix-valued moment problem on a union of a bounded interval and a point. The presented technique for solving the corresponding moment problem can potentially be used to determine degree bounds in the positivity certificates for matrix polynomials on compact sets <em>K</em> <span><span>[28, Theorem C]</span></span>.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"230 2","pages":"Article 108173"},"PeriodicalIF":0.8,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145981622","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":"Asymptotic vanishing of cohomology in triangulated categories","authors":"Petter Andreas Bergh ,&nbsp;David A. Jorgensen ,&nbsp;Peder Thompson","doi":"10.1016/j.jpaa.2026.108182","DOIUrl":"10.1016/j.jpaa.2026.108182","url":null,"abstract":"<div><div>Given a graded-commutative ring acting centrally on a triangulated category, our main result shows that if cohomology of a pair of objects of the triangulated category is finitely generated over the ring acting centrally, then the asymptotic vanishing of the cohomology is well-behaved. In particular, enough consecutive asymptotic vanishing of cohomology implies all eventual vanishing. Several key applications are also given.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"230 2","pages":"Article 108182"},"PeriodicalIF":0.8,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146079529","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":"Chromatic spherical invariant and Hennings invariant of 3-dimensional manifolds","authors":"J. Reina","doi":"10.1016/j.jpaa.2026.108170","DOIUrl":"10.1016/j.jpaa.2026.108170","url":null,"abstract":"<div><div>This paper establishes a relation between two invariants of 3-dimensional manifolds: the chromatic spherical invariant <span><math><mi>K</mi></math></span> and the Hennings-Kauffman-Radford invariant HKR. We show that, for a spherical Hopf algebra <em>H</em>, the invariant <span><math><mi>K</mi></math></span> associated to the pivotal category of finite-dimensional <em>H</em>-modules is equal to the invariant HKR associated to the Drinfeld double <span><math><mi>D</mi><mo>(</mo><mi>H</mi><mo>)</mo></math></span> of the same Hopf algebra.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"230 2","pages":"Article 108170"},"PeriodicalIF":0.8,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145950134","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":"Entropy and polynomial entropy of derived autoequivalences of derived discrete algebras","authors":"Tomasz Ciborski","doi":"10.1016/j.jpaa.2026.108185","DOIUrl":"10.1016/j.jpaa.2026.108185","url":null,"abstract":"<div><div>The aim of this paper is to calculate entropy in the sense of Dimitrov–Haiden–Katzarkov–Kontsevich and polynomial entropy as defined by Fan–Fu–Ouchi of derived autoequivalences of derived discrete algebras over an algebraically closed field.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"230 2","pages":"Article 108185"},"PeriodicalIF":0.8,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146079618","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":"Structure and symmetry of sally type semigroup rings","authors":"Srishti Singh,&nbsp;Hema Srinivasan","doi":"10.1016/j.jpaa.2026.108187","DOIUrl":"10.1016/j.jpaa.2026.108187","url":null,"abstract":"<div><div>Consider a numerical semigroup minimally generated by a subset of the interval <span><math><mo>[</mo><mi>e</mi><mo>,</mo><mn>2</mn><mi>e</mi><mo>−</mo><mn>1</mn><mo>]</mo></math></span> with multiplicity <em>e</em> and width <span><math><mi>e</mi><mo>−</mo><mn>1</mn></math></span>. Such numerical semigroups are called Sally type semigroups. We show that the defining ideals of these semigroup rings, when the embedding dimension is <span><math><mi>e</mi><mo>−</mo><mn>2</mn></math></span>, generically have the structure of the sum of two determinantal ideals. More generally, Sally type numerical semigroups with multiplicity <em>e</em> and embedding dimension <span><math><mi>d</mi><mo>=</mo><mi>e</mi><mo>−</mo><mi>k</mi></math></span> are obtained by introducing <em>k</em> gaps in the interval <span><math><mo>[</mo><mi>e</mi><mo>,</mo><mn>2</mn><mi>e</mi><mo>−</mo><mn>1</mn><mo>]</mo></math></span>. It is known that for <span><math><mi>k</mi><mo>=</mo><mn>2</mn></math></span>, there is precisely one such semigroup that is Gorenstein, and it happens when one deletes consecutive integers. Let <span><math><msubsup><mrow><mi>S</mi></mrow><mrow><mi>k</mi></mrow><mrow><mi>e</mi></mrow></msubsup><mo>(</mo><mi>j</mi><mo>)</mo></math></span> denote the Sally type numerical semigroup of multiplcity <em>e</em>, embedding dimension <span><math><mi>e</mi><mo>−</mo><mi>k</mi></math></span> obtained by deleting the <em>k</em> consecutive integers <span><math><mi>j</mi><mo>,</mo><mi>j</mi><mo>+</mo><mn>1</mn><mo>,</mo><mo>…</mo><mo>,</mo><mi>j</mi><mo>+</mo><mi>k</mi><mo>−</mo><mn>1</mn></math></span>. We prove that for any <span><math><mn>1</mn><mo>≤</mo><mi>k</mi><mo>&lt;</mo><mi>e</mi><mo>/</mo><mn>2</mn></math></span>, the semigroup <span><math><msubsup><mrow><mi>S</mi></mrow><mrow><mi>k</mi></mrow><mrow><mi>e</mi></mrow></msubsup><mo>(</mo><mi>j</mi><mo>)</mo></math></span> is Gorenstein if and only if <span><math><mi>j</mi><mo>=</mo><mi>k</mi></math></span>. We construct an explicit minimal free resolution of the semigroup ring of <span><math><msubsup><mrow><mi>S</mi></mrow><mrow><mi>k</mi></mrow><mrow><mi>e</mi></mrow></msubsup><mo>(</mo><mi>k</mi><mo>)</mo></math></span> and compute the Betti numbers. In general, we characterize when <span><math><msubsup><mrow><mi>S</mi></mrow><mrow><mi>k</mi></mrow><mrow><mi>e</mi></mrow></msubsup><mo>(</mo><mi>j</mi><mo>)</mo></math></span> are symmetric and construct minimal resolutions for these Gorenstein semigroup rings.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"230 2","pages":"Article 108187"},"PeriodicalIF":0.8,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146079525","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":"Dualities of Gaudin models with irregular singularities for general linear Lie (super)algebras","authors":"Wan Keng Cheong,&nbsp;Ngau Lam","doi":"10.1016/j.jpaa.2026.108195","DOIUrl":"10.1016/j.jpaa.2026.108195","url":null,"abstract":"<div><div>We prove an equivalence between the actions of the Gaudin algebras with irregular singularities for <span><math><msub><mrow><mi>gl</mi></mrow><mrow><mi>d</mi></mrow></msub></math></span> and <span><math><msub><mrow><mi>gl</mi></mrow><mrow><mi>p</mi><mo>+</mo><mi>m</mi><mo>|</mo><mi>q</mi><mo>+</mo><mi>n</mi></mrow></msub></math></span> on the Fock space of <span><math><mi>d</mi><mo>(</mo><mi>p</mi><mo>+</mo><mi>m</mi><mo>)</mo></math></span> bosonic and <span><math><mi>d</mi><mo>(</mo><mi>q</mi><mo>+</mo><mi>n</mi><mo>)</mo></math></span> fermionic oscillators. This establishes a duality of <span><math><mo>(</mo><msub><mrow><mi>gl</mi></mrow><mrow><mi>d</mi></mrow></msub><mo>,</mo><msub><mrow><mi>gl</mi></mrow><mrow><mi>p</mi><mo>+</mo><mi>m</mi><mo>|</mo><mi>q</mi><mo>+</mo><mi>n</mi></mrow></msub><mo>)</mo></math></span> for Gaudin models. As an application, we show that the Gaudin algebra with irregular singularities for <span><math><msub><mrow><mi>gl</mi></mrow><mrow><mi>p</mi><mo>+</mo><mi>m</mi><mo>|</mo><mi>q</mi><mo>+</mo><mi>n</mi></mrow></msub></math></span> acts cyclically on each weight space of a certain class of infinite-dimensional modules over a direct sum of Takiff superalgebras over <span><math><msub><mrow><mi>gl</mi></mrow><mrow><mi>p</mi><mo>+</mo><mi>m</mi><mo>|</mo><mi>q</mi><mo>+</mo><mi>n</mi></mrow></msub></math></span> and that the action is diagonalizable with a simple spectrum under a generic condition. We also study the classical versions of Gaudin algebras with irregular singularities and demonstrate a duality of <span><math><mo>(</mo><msub><mrow><mi>gl</mi></mrow><mrow><mi>d</mi></mrow></msub><mo>,</mo><msub><mrow><mi>gl</mi></mrow><mrow><mi>p</mi><mo>+</mo><mi>m</mi><mo>|</mo><mi>q</mi><mo>+</mo><mi>n</mi></mrow></msub><mo>)</mo></math></span> for classical Gaudin models.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"230 2","pages":"Article 108195"},"PeriodicalIF":0.8,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146174122","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}