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Categories of sets with infinite addition
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2025-02-01 DOI: 10.1016/j.jpaa.2025.107872
Pablo Andrés-Martínez , Chris Heunen
{"title":"Categories of sets with infinite addition","authors":"Pablo Andrés-Martínez ,&nbsp;Chris Heunen","doi":"10.1016/j.jpaa.2025.107872","DOIUrl":"10.1016/j.jpaa.2025.107872","url":null,"abstract":"<div><div>We consider sets with infinite addition, called Σ-monoids, and contribute to their literature in three ways. First, our definition subsumes those from previous works and allows us to relate them in terms of adjuctions between their categories. In particular, we discuss Σ-monoids with additive inverses. Second, we show that every Hausdorff commutative monoid is a Σ-monoid, and that there is a free Hausdorff commutative monoid for each Σ-monoid. Third, we prove that Σ-monoids have well-defined tensor products, unlike topological abelian groups.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 2","pages":"Article 107872"},"PeriodicalIF":0.7,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143163681","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Steenrod closed parameter ideals in the mod-2 cohomology of A4 and SO(3)
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2025-02-01 DOI: 10.1016/j.jpaa.2025.107899
Henrik Rüping , Marc Stephan , Ergün Yalçın
{"title":"Steenrod closed parameter ideals in the mod-2 cohomology of A4 and SO(3)","authors":"Henrik Rüping ,&nbsp;Marc Stephan ,&nbsp;Ergün Yalçın","doi":"10.1016/j.jpaa.2025.107899","DOIUrl":"10.1016/j.jpaa.2025.107899","url":null,"abstract":"<div><div>In this paper, we classify the parameter ideals in <span><math><msup><mrow><mi>H</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo>(</mo><mi>B</mi><msub><mrow><mi>A</mi></mrow><mrow><mn>4</mn></mrow></msub><mo>;</mo><msub><mrow><mi>F</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>)</mo></math></span> and in the Dickson algebra <span><math><msup><mrow><mi>H</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo>(</mo><mi>B</mi><mi>SO</mi><mo>(</mo><mn>3</mn><mo>)</mo><mo>;</mo><msub><mrow><mi>F</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>)</mo></math></span> that are closed under Steenrod operations. Consequently, we obtain restrictions on the dimensions <span><math><mi>n</mi><mo>,</mo><mi>m</mi></math></span> for which <span><math><msub><mrow><mi>A</mi></mrow><mrow><mn>4</mn></mrow></msub></math></span> (and <span><math><mi>SO</mi><mo>(</mo><mn>3</mn><mo>)</mo></math></span>) can act freely on <span><math><msup><mrow><mi>S</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>×</mo><msup><mrow><mi>S</mi></mrow><mrow><mi>m</mi></mrow></msup></math></span>.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 2","pages":"Article 107899"},"PeriodicalIF":0.7,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143387715","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Retraction notice to “Corrigendum to ‘On the fifth Singer algebraic transfer in a generic family of internal degree characterized by μ(n)=4’ [J. Pure Appl. Algebra 228 (2024) 107658]”
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2025-02-01 DOI: 10.1016/j.jpaa.2025.107908
Đặng Võ Phúc
{"title":"Retraction notice to “Corrigendum to ‘On the fifth Singer algebraic transfer in a generic family of internal degree characterized by μ(n)=4’ [J. Pure Appl. Algebra 228 (2024) 107658]”","authors":"Đặng Võ Phúc","doi":"10.1016/j.jpaa.2025.107908","DOIUrl":"10.1016/j.jpaa.2025.107908","url":null,"abstract":"","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 2","pages":"Article 107908"},"PeriodicalIF":0.7,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143508436","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Combinatorial model categories are equivalent to presentable quasicategories
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2025-02-01 DOI: 10.1016/j.jpaa.2024.107860
Dmitri Pavlov
{"title":"Combinatorial model categories are equivalent to presentable quasicategories","authors":"Dmitri Pavlov","doi":"10.1016/j.jpaa.2024.107860","DOIUrl":"10.1016/j.jpaa.2024.107860","url":null,"abstract":"<div><div>We establish a Dwyer–Kan equivalence of relative categories of combinatorial model categories, presentable quasicategories, and other models for locally presentable <span><math><mo>(</mo><mi>∞</mi><mo>,</mo><mn>1</mn><mo>)</mo></math></span>-categories. This implies that the underlying quasicategories of these relative categories are also equivalent. This article is also available at <span><span>arXiv:2110.04679v3</span><svg><path></path></svg></span>.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 2","pages":"Article 107860"},"PeriodicalIF":0.7,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143162773","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}
引用次数: 0
Intermediate categories for proper abelian subcategories
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2025-02-01 DOI: 10.1016/j.jpaa.2025.107892
Anders S. Kortegaard
{"title":"Intermediate categories for proper abelian subcategories","authors":"Anders S. Kortegaard","doi":"10.1016/j.jpaa.2025.107892","DOIUrl":"10.1016/j.jpaa.2025.107892","url":null,"abstract":"<div><div>Let <span><math><mi>A</mi></math></span> be an extension-closed proper abelian subcategory of a triangulated category <span><math><mi>T</mi></math></span>, with no negative 1 and 2 extensions. From this, two functors from <span><math><mi>Σ</mi><mi>A</mi><mo>⁎</mo><mi>A</mi></math></span> to <span><math><mi>A</mi></math></span> can be constructed giving a snake lemma mirroring that of homology without needing a t-structure.</div><div>We generalize the concept of intermediate categories, which originates from a paper by Enomoto and Saito, to the setting of proper abelian subcategories and show that under certain assumptions this collection is in bijection with torsion-free classes in <span><math><mi>A</mi></math></span>.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 2","pages":"Article 107892"},"PeriodicalIF":0.7,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143162793","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Generalizations of noncommutative Noether's problem
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2025-02-01 DOI: 10.1016/j.jpaa.2025.107896
João Fernando Schwarz
{"title":"Generalizations of noncommutative Noether's problem","authors":"João Fernando Schwarz","doi":"10.1016/j.jpaa.2025.107896","DOIUrl":"10.1016/j.jpaa.2025.107896","url":null,"abstract":"<div><div>Noether's problem is a classical and very important problem in algebra. It is an intrinsically interesting problem in invariant theory, but with far reaching applications in the sutdy of moduli spaces, PI-algebras, and the Inverse problem of Galois theory, among others. To obtain a noncommutative analogue of Noether's problem, one would need a significant skew field that shares a role similar to the field of rational functions. Given the importance of the Weyl fields due to Gelfand-Kirillov's Conjecture, in 2006 J. Alev and F. Dumas introduced what is nowadays called the Noncommutative Noether's problem. The aim of this article is to generalize the main result of <span><span>[12]</span></span> for more general versions of Noether's problem; and consider its analogue in prime characteristic.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 2","pages":"Article 107896"},"PeriodicalIF":0.7,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143351953","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}
引用次数: 0
On the conjugacy separability of ordinary and generalized Baumslag–Solitar groups
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2025-02-01 DOI: 10.1016/j.jpaa.2025.107906
E.V. Sokolov
{"title":"On the conjugacy separability of ordinary and generalized Baumslag–Solitar groups","authors":"E.V. Sokolov","doi":"10.1016/j.jpaa.2025.107906","DOIUrl":"10.1016/j.jpaa.2025.107906","url":null,"abstract":"<div><div>Let <span><math><mi>C</mi></math></span> be a class of groups. A group <em>X</em> is said to be residually a <span><math><mi>C</mi></math></span>-group (conjugacy <span><math><mi>C</mi></math></span>-separable) if, for any elements <span><math><mi>x</mi><mo>,</mo><mi>y</mi><mo>∈</mo><mi>X</mi></math></span> that are not equal (not conjugate in <em>X</em>), there exists a homomorphism <em>σ</em> of <em>X</em> onto a group from <span><math><mi>C</mi></math></span> such that the elements <em>xσ</em> and <em>yσ</em> are still not equal (respectively, not conjugate in <em>Xσ</em>). A generalized Baumslag–Solitar group or GBS-group is the fundamental group of a finite connected graph of groups whose vertex and edge groups are all infinite cyclic. An ordinary Baumslag–Solitar group is the GBS-group that corresponds to a graph containing only one vertex and one loop. Suppose that the class <span><math><mi>C</mi></math></span> consists of periodic groups and is closed under taking subgroups and unrestricted wreath products. We prove that a non-solvable GBS-group is conjugacy <span><math><mi>C</mi></math></span>-separable if and only if it is residually a <span><math><mi>C</mi></math></span>-group. We also find a criterion for a solvable GBS-group to be conjugacy <span><math><mi>C</mi></math></span>-separable. As a corollary, we prove that an arbitrary GBS-group is conjugacy (finite) separable if and only if it is residually finite.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 2","pages":"Article 107906"},"PeriodicalIF":0.7,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143394582","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}
引用次数: 0
The Adams operators on connected graded Hopf algebras
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2025-02-01 DOI: 10.1016/j.jpaa.2025.107877
Y.-Y. Li, G.-S. Zhou
{"title":"The Adams operators on connected graded Hopf algebras","authors":"Y.-Y. Li,&nbsp;G.-S. Zhou","doi":"10.1016/j.jpaa.2025.107877","DOIUrl":"10.1016/j.jpaa.2025.107877","url":null,"abstract":"<div><div>The Adams operators on a Hopf algebra <em>H</em> are the convolution powers of the identity map of <em>H</em>. They are also called Hopf powers or Sweedler powers. It is a natural family of operators on <em>H</em> that contains the antipode. We study the linear properties of the Adams operators when <span><math><mi>H</mi><mo>=</mo><msub><mrow><mo>⨁</mo></mrow><mrow><mi>m</mi><mo>∈</mo><mi>N</mi></mrow></msub><msub><mrow><mi>H</mi></mrow><mrow><mi>m</mi></mrow></msub></math></span> is connected graded. The main result is that for any of such <em>H</em>, there exist a PBW type homogeneous basis and a natural total order on it such that the restrictions <span><math><msub><mrow><mi>Ψ</mi></mrow><mrow><mi>n</mi></mrow></msub><msub><mrow><mo>|</mo></mrow><mrow><msub><mrow><mi>H</mi></mrow><mrow><mi>m</mi></mrow></msub></mrow></msub></math></span> of the Adams operators are simultaneously upper triangularizable with respect to this ordered basis. Moreover, the diagonal coefficients are determined in terms of <em>n</em> and a combinatorial number assigned to the basis elements. As an immediate consequence, we obtain a complete description of the characteristic polynomial of <span><math><msub><mrow><mi>Ψ</mi></mrow><mrow><mi>n</mi></mrow></msub><msub><mrow><mo>|</mo></mrow><mrow><msub><mrow><mi>H</mi></mrow><mrow><mi>m</mi></mrow></msub></mrow></msub></math></span>, both on eigenvalues and their multiplicities, when <em>H</em> is locally finite and the base field is of characteristic zero. It recovers the main result of the paper <span><span>[2]</span></span> by Aguiar and Lauve, where the approach is different from ours.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 2","pages":"Article 107877"},"PeriodicalIF":0.7,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143163683","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}
引用次数: 0
Symmetric hyperbolic polynomials
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2025-02-01 DOI: 10.1016/j.jpaa.2025.107869
Grigoriy Blekherman, Julia Lindberg, Kevin Shu
{"title":"Symmetric hyperbolic polynomials","authors":"Grigoriy Blekherman,&nbsp;Julia Lindberg,&nbsp;Kevin Shu","doi":"10.1016/j.jpaa.2025.107869","DOIUrl":"10.1016/j.jpaa.2025.107869","url":null,"abstract":"<div><div>Hyperbolic polynomials have been of recent interest due to applications in a wide variety of fields. We seek to better understand these polynomials in the case when they are symmetric, i.e. invariant under all permutations of the variables. We give a complete characterization of the set of symmetric hyperbolic polynomials of degree 3, and a large class of symmetric hyperbolic polynomials of degree 4. For a class of polynomials, which we call hook-shaped, we relate symmetric hyperbolic polynomials to a class of linear maps of univariate polynomials preserving hyperbolicity, and give evidence toward a beautiful characterization of all such hook-shaped symmetric hyperbolic polynomials. We show that hyperbolicity cones of a class of symmetric hyperbolic polynomials, including all symmetric hyperbolic cubics, are spectrahedral. Finally, we connect testing hyperbolicity of a symmetric polynomial to the degree principle for symmetric nonnegative polynomials.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 2","pages":"Article 107869"},"PeriodicalIF":0.7,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143162787","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}
引用次数: 0
Minimal cellular resolutions of powers of matching field ideals
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2025-02-01 DOI: 10.1016/j.jpaa.2025.107893
Oliver Clarke , Fatemeh Mohammadi
{"title":"Minimal cellular resolutions of powers of matching field ideals","authors":"Oliver Clarke ,&nbsp;Fatemeh Mohammadi","doi":"10.1016/j.jpaa.2025.107893","DOIUrl":"10.1016/j.jpaa.2025.107893","url":null,"abstract":"<div><div>We study a family of monomial ideals, called block diagonal matching field ideals, which arise as monomial Gröbner degenerations of determinantal ideals. Our focus is on the minimal free resolutions of these ideals and all of their powers. Initially, we establish their linear quotient property and compute their Betti numbers, illustrating that their minimal free resolution is supported on a regular CW complex. Our proof relies on the results of Herzog and Takayama, demonstrating that ideals with a linear quotient property have a minimal free resolution, and on the construction by Dochtermann and Mohammadi of cellular realizations of these resolutions. We begin by proving the linear quotient property for each power of such an ideal. Subsequently, we show that their corresponding decomposition map is regular, resulting in a minimal cellular resolution. Finally, we demonstrate that distinct decomposition maps lead to different cellular complexes with the same face numbers.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 2","pages":"Article 107893"},"PeriodicalIF":0.7,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143162789","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}
引用次数: 0
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