{"title":"On some ideal structure of Leavitt path algebras with coefficients in integral domains","authors":"Trinh Thanh Deo, Vo Thanh Chi","doi":"10.24330/ieja.1229771","DOIUrl":null,"url":null,"abstract":"In this paper, we present results concerning the structure of the ideals in the Leavitt path algebra of a (countable) directed graph with coefficients in an integral domain, such as, describing the set of generators for an ideal; the necessary and sufficient conditions for an ideal to be prime; the necessary and sufficient conditions for a Leavitt path algebra to be simple. Besides, some other interesting properties of ideal structure in a Leavitt path algebra are also mentioned.","PeriodicalId":43749,"journal":{"name":"International Electronic Journal of Algebra","volume":" ","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2023-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Electronic Journal of Algebra","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.24330/ieja.1229771","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 2
Abstract
In this paper, we present results concerning the structure of the ideals in the Leavitt path algebra of a (countable) directed graph with coefficients in an integral domain, such as, describing the set of generators for an ideal; the necessary and sufficient conditions for an ideal to be prime; the necessary and sufficient conditions for a Leavitt path algebra to be simple. Besides, some other interesting properties of ideal structure in a Leavitt path algebra are also mentioned.
期刊介绍：
The International Electronic Journal of Algebra is published twice a year. IEJA is reviewed by Mathematical Reviews, MathSciNet, Zentralblatt MATH, Current Mathematical Publications. IEJA seeks previously unpublished papers that contain: Module theory Ring theory Group theory Algebras Comodules Corings Coalgebras Representation theory Number theory.
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