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Journal of Pure and Applied Algebra最新文献

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Computation of the classifying ring of formal modules 形式模的分类环的计算
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2025-04-11 DOI: 10.1016/j.jpaa.2025.107975
A. Salch
{"title":"Computation of the classifying ring of formal modules","authors":"A. Salch","doi":"10.1016/j.jpaa.2025.107975","DOIUrl":"10.1016/j.jpaa.2025.107975","url":null,"abstract":"<div><div>In this paper, we develop general machinery for computing the classifying ring <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>A</mi></mrow></msup></math></span> of one-dimensional formal <em>A</em>-modules, for various commutative rings <em>A</em>. We then apply the machinery to obtain calculations of <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>A</mi></mrow></msup></math></span> for various number rings and cyclic group rings <em>A</em>. This includes the first full calculations of the ring <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>A</mi></mrow></msup></math></span> in cases in which it fails to be a polynomial algebra. We also derive consequences for the solvability of some lifting and extension problems.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 6","pages":"Article 107975"},"PeriodicalIF":0.7,"publicationDate":"2025-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143844084","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
Groups with BCℓ-commutator relations 具有BC -换向子关系的群
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2025-04-10 DOI: 10.1016/j.jpaa.2025.107966
Egor Voronetsky
{"title":"Groups with BCℓ-commutator relations","authors":"Egor Voronetsky","doi":"10.1016/j.jpaa.2025.107966","DOIUrl":"10.1016/j.jpaa.2025.107966","url":null,"abstract":"<div><div>Isotropic odd unitary groups generalize Chevalley groups of classical types over commutative rings and their twisted forms. Such groups have root subgroups parameterized by a root system <span><math><msub><mrow><mi>BC</mi></mrow><mrow><mi>ℓ</mi></mrow></msub></math></span> and may be constructed by so-called odd form rings with Peirce decompositions. We show the converse: if a group <em>G</em> has root subgroups indexed by roots of <span><math><msub><mrow><mi>BC</mi></mrow><mrow><mi>ℓ</mi></mrow></msub></math></span> and satisfying natural conditions, then there is a homomorphism <figure><img></figure> inducing isomorphisms on the root subgroups, where <figure><img></figure> is the odd unitary Steinberg group constructed by an odd form ring <span><math><mo>(</mo><mi>R</mi><mo>,</mo><mi>Δ</mi><mo>)</mo></math></span> with a Peirce decomposition. For groups with root subgroups indexed by <span><math><msub><mrow><mi>A</mi></mrow><mrow><mi>ℓ</mi></mrow></msub></math></span> (the already known case) the resulting odd form ring is essentially a generalized matrix ring.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 7","pages":"Article 107966"},"PeriodicalIF":0.7,"publicationDate":"2025-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143844095","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
Hilbert scheme of a pair of skew lines on cubic threefolds 三次曲面上一对斜线的希尔伯特格式
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2025-04-10 DOI: 10.1016/j.jpaa.2025.107971
Yilong Zhang
{"title":"Hilbert scheme of a pair of skew lines on cubic threefolds","authors":"Yilong Zhang","doi":"10.1016/j.jpaa.2025.107971","DOIUrl":"10.1016/j.jpaa.2025.107971","url":null,"abstract":"<div><div>Two general lines on a smooth cubic threefold <em>X</em> are disjoint and determine an irreducible component of the Hilbert scheme of <em>X</em>. We prove that this component is smooth and isomorphic to the Hilbert scheme of two points of the Fano varieties of lines of <em>X</em>. We also study its relation to the geometry of lines and singularities on the hyperplane sections of <em>X</em> and its relation to Bridgeland moduli spaces.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 6","pages":"Article 107971"},"PeriodicalIF":0.7,"publicationDate":"2025-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143854737","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 third homology of projective special linear group of degree two 二阶射影特殊线性群的第三同调
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2025-04-10 DOI: 10.1016/j.jpaa.2025.107965
Behrooz Mirzaii , Elvis Torres Pérez
{"title":"The third homology of projective special linear group of degree two","authors":"Behrooz Mirzaii ,&nbsp;Elvis Torres Pérez","doi":"10.1016/j.jpaa.2025.107965","DOIUrl":"10.1016/j.jpaa.2025.107965","url":null,"abstract":"<div><div>In this paper we investigate the third homology of the projective special linear group <span><math><msub><mrow><mi>PSL</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>(</mo><mi>A</mi><mo>)</mo></math></span>. As a result of our investigation we prove a projective refined Bloch-Wigner exact sequence over certain class of rings. The projective Bloch-Wigner exact sequence over an algebraically closed field of characteristic zero is a classical result and has many applications in algebra, number theory and geometry.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 6","pages":"Article 107965"},"PeriodicalIF":0.7,"publicationDate":"2025-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143843968","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
Infinitely many non-conjugate braid representatives of links 连杆的无穷多个非共轭辫状表示
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2025-04-10 DOI: 10.1016/j.jpaa.2025.107964
Reiko Shinjo , Alexander Stoimenow
{"title":"Infinitely many non-conjugate braid representatives of links","authors":"Reiko Shinjo ,&nbsp;Alexander Stoimenow","doi":"10.1016/j.jpaa.2025.107964","DOIUrl":"10.1016/j.jpaa.2025.107964","url":null,"abstract":"<div><div>We prove that under a fairly general condition (that the edge strands are not fixed by the braid permutation) an iterated exchange move gives infinitely many non-conjugate braid representatives of links. More precisely, almost all braids obtained by iterated positive exchange moves are pairwise non-conjugate. As a consequence, every link with no trivial components has infinitely many conjugacy classes of <em>n</em>-braid representatives if and only if it has one admitting an exchange move.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 7","pages":"Article 107964"},"PeriodicalIF":0.7,"publicationDate":"2025-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143863588","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
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 关于循环和合并树
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 广义周期性定理
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 在纤维伯恩赛德环上，有纤维变化图和循环纤维群
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 一个遗传完全扭转对的模型结构
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
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