{"title":"A Generalization of the Nilpotency Index of the Radical of the Module Category of an Algebra","authors":"Claudia Chaio, Pamela Suarez","doi":"10.1007/s10468-024-10307-4","DOIUrl":null,"url":null,"abstract":"<div><p>Let <i>A</i> be a finite dimensional representation-finite algebra over an algebraically closed field. The aim of this work is to generalize the results proven in [8]. Precisely, we determine which vertices of <span>\\(Q_A\\)</span> are sufficient to be considered in order to compute the nilpotency index of the radical of the module category of a monomial algebra and a toupie algebra <i>A</i>, when the Auslander-Reiten quiver is not necessarily a component with length.</p></div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"28 1","pages":"81 - 99"},"PeriodicalIF":0.6000,"publicationDate":"2025-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Algebras and Representation Theory","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10468-024-10307-4","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
Let A be a finite dimensional representation-finite algebra over an algebraically closed field. The aim of this work is to generalize the results proven in [8]. Precisely, we determine which vertices of \(Q_A\) are sufficient to be considered in order to compute the nilpotency index of the radical of the module category of a monomial algebra and a toupie algebra A, when the Auslander-Reiten quiver is not necessarily a component with length.
期刊介绍：
Algebras and Representation Theory features carefully refereed papers relating, in its broadest sense, to the structure and representation theory of algebras, including Lie algebras and superalgebras, rings of differential operators, group rings and algebras, C*-algebras and Hopf algebras, with particular emphasis on quantum groups.
The journal contains high level, significant and original research papers, as well as expository survey papers written by specialists who present the state-of-the-art of well-defined subjects or subdomains. Occasionally, special issues on specific subjects are published as well, the latter allowing specialists and non-specialists to quickly get acquainted with new developments and topics within the field of rings, algebras and their applications.
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