{"title":"Ideally finite Leibniz algebras","authors":"L. A. Kurdachenko, I. Ya. Subbotin","doi":"10.12958/adm2139","DOIUrl":null,"url":null,"abstract":"The aim of this paper is to consider Leibniz algebras, whose principal ideals are finite dimensional. We prove that the derived ideal of L has finite dimension if every principal ideal of a Leibniz algebra L has dimension at most b, where b is a fixed positive integer.","PeriodicalId":364397,"journal":{"name":"Algebra and Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Algebra and Discrete Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.12958/adm2139","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
The aim of this paper is to consider Leibniz algebras, whose principal ideals are finite dimensional. We prove that the derived ideal of L has finite dimension if every principal ideal of a Leibniz algebra L has dimension at most b, where b is a fixed positive integer.