Journal of Pure and Applied Algebra最新文献_第8页

The centralizer of a locally nilpotent R-derivation of the polynomial R-algebra in two variables 二变量多项式 R 代数的局部零势 R 派生的中心子

IF 0.7 2区数学

Journal of Pure and Applied Algebra Pub Date : 2024-10-22 DOI: 10.1016/j.jpaa.2024.107828

M'hammed El Kahoui, Najoua Essamaoui, Mustapha Ouali

{"title":"The centralizer of a locally nilpotent R-derivation of the polynomial R-algebra in two variables","authors":"M'hammed El Kahoui, Najoua Essamaoui, Mustapha Ouali","doi":"10.1016/j.jpaa.2024.107828","DOIUrl":"10.1016/j.jpaa.2024.107828","url":null,"abstract":"<div><div>Let R be an integral domain containing <math><mi>Q</mi></math> and ξ be an irreducible nontrivial locally nilpotent R-derivation of the polynomial R-algebra A in two variables. In this paper we investigate the group <math><msub><mrow><mi>Aut</mi></mrow><mrow><mi>R</mi></mrow></msub><mo>(</mo><mi>A</mi><mo>,</mo><mi>ξ</mi><mo>)</mo></math> of R-automorphisms of A which commute with ξ. In the case R is a unique factorization domain and the plinth ideal of ξ is principal we give a complete description of the subgroup <math><msub><mrow><mi>SAut</mi></mrow><mrow><mi>R</mi></mrow></msub><mo>(</mo><mi>A</mi><mo>,</mo><mi>ξ</mi><mo>)</mo></math> of <math><msub><mrow><mi>Aut</mi></mrow><mrow><mi>R</mi></mrow></msub><mo>(</mo><mi>A</mi><mo>,</mo><mi>ξ</mi><mo>)</mo></math> consisting of Jacobian one automorphisms. If moreover R contains a field K such that the group of units of R is <math><msup><mrow><mi>K</mi></mrow><mrow><mo>⋆</mo></mrow></msup></math> we prove that <math><msub><mrow><mi>Aut</mi></mrow><mrow><mi>R</mi></mrow></msub><mo>(</mo><mi>A</mi><mo>,</mo><mi>ξ</mi><mo>)</mo><mo>=</mo><msub><mrow><mi>SAut</mi></mrow><mrow><mi>R</mi></mrow></msub><mo>(</mo><mi>A</mi><mo>,</mo><mi>ξ</mi><mo>)</mo></math>.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 1","pages":"Article 107828"},"PeriodicalIF":0.7,"publicationDate":"2024-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142552130","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

Characterization of affine Gm-surfaces of hyperbolic type 双曲型仿射 Gm 曲面的特征

IF 0.7 2区数学

Journal of Pure and Applied Algebra Pub Date : 2024-10-22 DOI: 10.1016/j.jpaa.2024.107829

Andriy Regeta

引用次数: 0

Representations of quantum lattice vertex algebras 量子格顶点代数的表示

IF 0.7 2区数学

Journal of Pure and Applied Algebra Pub Date : 2024-10-22 DOI: 10.1016/j.jpaa.2024.107832

Fei Kong

引用次数: 0

Characteristic modules and Gorenstein (co-)homological dimension of groups 特征模块和群的戈伦斯坦（共）同维度

IF 0.7 2区数学

Journal of Pure and Applied Algebra Pub Date : 2024-10-22 DOI: 10.1016/j.jpaa.2024.107830

Ioannis Emmanouil, Olympia Talelli

{"title":"Characteristic modules and Gorenstein (co-)homological dimension of groups","authors":"Ioannis Emmanouil, Olympia Talelli","doi":"10.1016/j.jpaa.2024.107830","DOIUrl":"10.1016/j.jpaa.2024.107830","url":null,"abstract":"<div><div>In this paper, we examine the Gorenstein dimension of modules over the group algebra kG of a group G with coefficients in a commutative ring k. As a Gorenstein analogue of the classical case, we bound this dimension in terms of the Gorenstein dimension of the underlying k-module and the Gorenstein dimension of G over k. Our method is based on the notion of a characteristic module for G, introduced by the second author, and uses the stability properties of the Gorenstein categories. We also examine the class of hierarchically decomposable groups defined by Kropholler and use the module of bounded <math><mi>Z</mi></math>-valued functions on such a group G to characterize the Gorenstein flat <math><mi>Z</mi><mi>G</mi></math>-modules, in terms of flat modules, and the Gorenstein injective <math><mi>Z</mi><mi>G</mi></math>-modules, in terms of injective modules (by complete analogy with the characterization of Gorenstein projective <math><mi>Z</mi><mi>G</mi></math>-modules, in terms of projective modules, obtained by Dembegioti and the second author). It follows that, for a group G in Kropholler's class, (a) any Gorenstein projective <math><mi>Z</mi><mi>G</mi></math>-module is Gorenstein flat and (b) a <math><mi>Z</mi><mi>G</mi></math>-module is Gorenstein flat if its Pontryagin dual module is Gorenstein injective.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 1","pages":"Article 107830"},"PeriodicalIF":0.7,"publicationDate":"2024-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142552131","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

A binary tree of complete intersections with the strong Lefschetz property 具有强列夫谢茨特性的二叉完全相交树

IF 0.7 2区数学

Journal of Pure and Applied Algebra Pub Date : 2024-10-16 DOI: 10.1016/j.jpaa.2024.107825

Tadahito Harima , Satoru Isogawa , Junzo Watanabe

引用次数: 0

Periodic derived Hall algebras of hereditary abelian categories 遗传无性类的周期派生霍尔代数

IF 0.7 2区数学

Journal of Pure and Applied Algebra Pub Date : 2024-10-16 DOI: 10.1016/j.jpaa.2024.107824

Haicheng Zhang

引用次数: 0

On Krull-Gabriel dimension of cluster repetitive categories and cluster-tilted algebras 关于簇重复范畴和簇倾斜代数的克鲁尔-加布里埃尔维度

IF 0.7 2区数学

Journal of Pure and Applied Algebra Pub Date : 2024-10-16 DOI: 10.1016/j.jpaa.2024.107823

Alicja Jaworska-Pastuszak, Grzegorz Pastuszak, Grzegorz Bobiński

引用次数: 0

The Modular Isomorphism Problem – the alternative perspective on counterexamples 模块同构问题--反例的另一种视角

IF 0.7 2区数学

Journal of Pure and Applied Algebra Pub Date : 2024-10-16 DOI: 10.1016/j.jpaa.2024.107826

Czesław Bagiński, Kamil Zabielski

引用次数: 0

Rouquier dimension versus global dimension 鲁基耶维度与全球维度

IF 0.7 2区数学

Journal of Pure and Applied Algebra Pub Date : 2024-10-15 DOI: 10.1016/j.jpaa.2024.107827

Greg Stevenson

引用次数: 0

Torsion-simple objects in abelian categories 阿贝尔范畴中的扭转简单对象

IF 0.7 2区数学

Journal of Pure and Applied Algebra Pub Date : 2024-10-09 DOI: 10.1016/j.jpaa.2024.107818

Sergio Pavon

引用次数: 0