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Journal of Pure and Applied Algebra最新文献

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Primitive two-dimensional prime-universality of quadratic forms 二次函数形式的原始二维素数通用性
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2025-04-10 DOI: 10.1016/j.jpaa.2025.107968
N. Budarina
{"title":"Primitive two-dimensional prime-universality of quadratic forms","authors":"N. Budarina","doi":"10.1016/j.jpaa.2025.107968","DOIUrl":"10.1016/j.jpaa.2025.107968","url":null,"abstract":"<div><div>In this paper we give a local description of quadratic forms that primitively represent all binary forms with specific Jordan decompositions over the odd ring <span><math><msub><mrow><mi>Z</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span>. As an application of the local results, we prove a result related to a two-dimensional generalization of primitive prime-universality.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 6","pages":"Article 107968"},"PeriodicalIF":0.7,"publicationDate":"2025-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143829399","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 cycles and merge trees
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2025-04-09 DOI: 10.1016/j.jpaa.2025.107967
Julian Brüggemann , Nicholas A. Scoville
{"title":"On cycles and merge trees","authors":"Julian Brüggemann ,&nbsp;Nicholas A. Scoville","doi":"10.1016/j.jpaa.2025.107967","DOIUrl":"10.1016/j.jpaa.2025.107967","url":null,"abstract":"<div><div>In this paper, we extend the notion of a merge tree to that of a generalized merge tree, a merge tree that includes 1-dimensional cycle birth information. Given a discrete Morse function on a 1-dimensional CW complex, i.e., a multigraph, we construct the induced generalized merge tree. We give several notions of equivalence of discrete Morse functions based on the induced generalized merge tree and how these notions relate to one another. As a consequence, we obtain a complete solution to the inverse problem between discrete Morse functions on 1-dimensional CW complexes and generalized merge trees. After characterizing which generalized merge trees can be induced by a discrete Morse function on a simple graph, we give an algorithm based on the induced generalized merge tree of a discrete Morse function <span><math><mi>f</mi><mo>:</mo><mi>X</mi><mo>→</mo><mi>R</mi></math></span> that cancels the critical cells of <em>f</em> and replaces it with an optimal discrete Morse function.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 7","pages":"Article 107967"},"PeriodicalIF":0.7,"publicationDate":"2025-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143828970","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
Generalized periodicity theorems
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2025-03-27 DOI: 10.1016/j.jpaa.2025.107962
Leonid Positselski
{"title":"Generalized periodicity theorems","authors":"Leonid Positselski","doi":"10.1016/j.jpaa.2025.107962","DOIUrl":"10.1016/j.jpaa.2025.107962","url":null,"abstract":"<div><div>Let <em>R</em> be a ring and <span><math><mi>S</mi></math></span> be a class of strongly finitely presented (<span><math><msub><mrow><mi>FP</mi></mrow><mrow><mo>∞</mo></mrow></msub></math></span>) <em>R</em>-modules closed under extensions, direct summands, and syzygies. Let <span><math><mo>(</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo>)</mo></math></span> be the (hereditary complete) cotorsion pair generated by <span><math><mi>S</mi></math></span> in <span><math><mi>Mod--</mi><mspace></mspace><mi>R</mi></math></span>, and let <span><math><mo>(</mo><mi>C</mi><mo>,</mo><mi>D</mi><mo>)</mo></math></span> be the (also hereditary complete) cotorsion pair in which <span><math><mi>C</mi><mo>=</mo><munder><mi>lim</mi><mo>→</mo></munder><mi>A</mi><mo>=</mo><munder><mi>lim</mi><mo>→</mo></munder><mi>S</mi></math></span>. We show that any <span><math><mi>A</mi></math></span>-periodic module in <span><math><mi>C</mi></math></span> belongs to <span><math><mi>A</mi></math></span>, and any <span><math><mi>D</mi></math></span>-periodic module in <span><math><mi>B</mi></math></span> belongs to <span><math><mi>D</mi></math></span>. Further generalizations of both results are obtained, so that we get a common generalization of the flat/projective and fp-projective periodicity theorems, as well as a common generalization of the fp-injective/injective and cotorsion periodicity theorems. Both are applicable to modules over an arbitrary ring, and in fact, to Grothendieck categories.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 7","pages":"Article 107962"},"PeriodicalIF":0.7,"publicationDate":"2025-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143776896","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 fibered Burnside rings, fiber change maps and cyclic fiber groups
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2025-03-25 DOI: 10.1016/j.jpaa.2025.107961
Benjamín García, Alberto G. Raggi-Cárdenas
{"title":"On fibered Burnside rings, fiber change maps and cyclic fiber groups","authors":"Benjamín García,&nbsp;Alberto G. Raggi-Cárdenas","doi":"10.1016/j.jpaa.2025.107961","DOIUrl":"10.1016/j.jpaa.2025.107961","url":null,"abstract":"<div><div>Fibered Burnside rings appear as Grothendieck rings of fibered permutation representations of a finite group, generalizing Burnside rings and monomial representation rings. Their species, primitive idempotents and their conductors are of particular interest in representation theory as they encode information related to the structure of the group. In this note, we introduce fiber change maps between fibered Burnside rings, and we present results on their functoriality and naturality with respect to biset operations. We present some advances on the conductors for cyclic fiber groups, and fully determine them in particular cases, covering a wide range of interesting examples.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 6","pages":"Article 107961"},"PeriodicalIF":0.7,"publicationDate":"2025-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143759663","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
Model structure from one hereditary complete cotorsion pair
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2025-03-25 DOI: 10.1016/j.jpaa.2025.107958
Jian Cui, Xue-Song Lu, Pu Zhang
{"title":"Model structure from one hereditary complete cotorsion pair","authors":"Jian Cui,&nbsp;Xue-Song Lu,&nbsp;Pu Zhang","doi":"10.1016/j.jpaa.2025.107958","DOIUrl":"10.1016/j.jpaa.2025.107958","url":null,"abstract":"<div><div>In contrast with the Hovey correspondence of abelian model structures from two complete cotorsion pairs, Beligiannis and Reiten give a construction of model structures on abelian categories from one hereditary complete cotorsion pair. The aim of this paper is to extend this result to weakly idempotent complete exact categories, by adding the condition of heredity of the complete cotorsion pair. In fact, even for abelian categories, this condition of heredity should be added. This construction really gives model structures which are not necessarily exact in the sense of Gillespie. The correspondence of Beligiannis and Reiten of weakly projective model structures also holds for weakly idempotent complete exact categories.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 7","pages":"Article 107958"},"PeriodicalIF":0.7,"publicationDate":"2025-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143761147","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
Module monoidal categories as categorification of associative algebras
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2025-03-24 DOI: 10.1016/j.jpaa.2025.107959
Sebastian Heinrich
{"title":"Module monoidal categories as categorification of associative algebras","authors":"Sebastian Heinrich","doi":"10.1016/j.jpaa.2025.107959","DOIUrl":"10.1016/j.jpaa.2025.107959","url":null,"abstract":"<div><div>In <span><span>[12]</span></span>, the notion of a module tensor category was introduced as a braided monoidal central functor <span><math><mi>F</mi><mo>:</mo><mi>V</mi><mo>⟶</mo><mi>T</mi></math></span> from a braided monoidal category <span><math><mi>V</mi></math></span> to a monoidal category <span><math><mi>T</mi></math></span>, which is a monoidal functor <span><math><mi>F</mi><mo>:</mo><mi>V</mi><mo>⟶</mo><mi>T</mi></math></span> together with a braided monoidal lift <span><math><msup><mrow><mi>F</mi></mrow><mrow><mi>Z</mi></mrow></msup><mo>:</mo><mi>V</mi><mo>⟶</mo><mi>Z</mi><mo>(</mo><mi>T</mi><mo>)</mo></math></span> to the Drinfeld center of <span><math><mi>T</mi></math></span>. This is a categorification of a unital associative algebra <em>A</em> over a commutative ring <em>R</em> via a ring homomorphism <span><math><mi>f</mi><mo>:</mo><mi>R</mi><mo>⟶</mo><mi>Z</mi><mo>(</mo><mi>A</mi><mo>)</mo></math></span> into the center of <em>A</em>. In this paper, we want to categorify the characterization of an associative algebra as a (not necessarily unital) ring <em>A</em> together with an <em>R</em>–module structure over a commutative ring <em>R</em>, such that multiplication in <em>A</em> and action of <em>R</em> on <em>A</em> are compatible. In doing so, we introduce the more general notion of <em>non–unital module monoidal categories</em> and obtain 2–categories of non–unital and unital module monoidal categories, their functors and natural transformations. We will show that in the unital case the latter definition is equivalent to the definition in <span><span>[12]</span></span> by explicitly writing down an equivalence of 2–categories.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 7","pages":"Article 107959"},"PeriodicalIF":0.7,"publicationDate":"2025-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143738875","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
Injective generation for graded rings
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2025-03-24 DOI: 10.1016/j.jpaa.2025.107960
Panagiotis Kostas, Chrysostomos Psaroudakis
{"title":"Injective generation for graded rings","authors":"Panagiotis Kostas,&nbsp;Chrysostomos Psaroudakis","doi":"10.1016/j.jpaa.2025.107960","DOIUrl":"10.1016/j.jpaa.2025.107960","url":null,"abstract":"<div><div>In this paper we investigate injective generation for graded rings. We first examine the relation between injective generation and graded injective generation for graded rings. We then reduce the study of injective generation for graded rings to the study of injective generation for certain Morita context rings and we provide sufficient conditions for injective generation of the latter. We then provide necessary and sufficient conditions so that injectives generate for tensor rings and for trivial extension rings. We provide two proofs for the class of tensor rings, one uses covering theory and the other uses the framework of cleft extensions of module categories. We finally prove injective generation for twisted tensor products of finite dimensional algebras.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 7","pages":"Article 107960"},"PeriodicalIF":0.7,"publicationDate":"2025-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143761148","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
Affine pavings of quiver flag varieties
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2025-03-21 DOI: 10.1016/j.jpaa.2025.107953
Xiaoxiang Zhou
{"title":"Affine pavings of quiver flag varieties","authors":"Xiaoxiang Zhou","doi":"10.1016/j.jpaa.2025.107953","DOIUrl":"10.1016/j.jpaa.2025.107953","url":null,"abstract":"<div><div>In this article, we construct affine pavings for quiver partial flag varieties when the quiver is of Dynkin type. To achieve our results, we extend methods from Cerulli-Irelli–Esposito–Franzen–Reineke and Maksimau as well as techniques from Auslander–Reiten theory.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 6","pages":"Article 107953"},"PeriodicalIF":0.7,"publicationDate":"2025-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143704285","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
The pro-nilpotent Lawrence-Krammer-Bigelow representation
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2025-03-19 DOI: 10.1016/j.jpaa.2025.107952
Martin Palmer , Arthur Soulié
{"title":"The pro-nilpotent Lawrence-Krammer-Bigelow representation","authors":"Martin Palmer ,&nbsp;Arthur Soulié","doi":"10.1016/j.jpaa.2025.107952","DOIUrl":"10.1016/j.jpaa.2025.107952","url":null,"abstract":"<div><div>We construct a 3-variable enrichment of the Lawrence-Krammer-Bigelow (LKB) representation of the braid groups, which is the limit of a pro-nilpotent tower of representations having the original LKB representation as its bottom layer. We also construct analogous pro-nilpotent towers of representations of surface braid groups and loop braid groups.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 6","pages":"Article 107952"},"PeriodicalIF":0.7,"publicationDate":"2025-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143738976","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
The isomorphism problem for rational group algebras of finite metacyclic groups
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2025-03-19 DOI: 10.1016/j.jpaa.2025.107951
Àngel García-Blázquez, Ángel del Río
{"title":"The isomorphism problem for rational group algebras of finite metacyclic groups","authors":"Àngel García-Blázquez,&nbsp;Ángel del Río","doi":"10.1016/j.jpaa.2025.107951","DOIUrl":"10.1016/j.jpaa.2025.107951","url":null,"abstract":"<div><div>We prove that if two finite metacyclic groups have isomorphic rational group algebras, then they are isomorphic. This contributes to understand where the line separating positive and negative solutions to the Isomorphism Problem for group algebras lies.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 6","pages":"Article 107951"},"PeriodicalIF":0.7,"publicationDate":"2025-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143683882","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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