{"title":"Direct summands of Goldie extending elements in modular lattices","authors":"R. Shroff","doi":"10.21136/mb.2021.0181-20","DOIUrl":null,"url":null,"abstract":"In this paper some results on direct summands of Goldie extending elements are studied in a modular lattice. An element a of a lattice L with 0 is said to be a Goldie extending element if and only if for every b 6 a there exists a direct summand c of a such that b ∧ c is essential in both b and c. Some characterizations of decomposition of a Goldie extending element in a modular lattice are obtained.","PeriodicalId":45392,"journal":{"name":"Mathematica Bohemica","volume":null,"pages":null},"PeriodicalIF":0.3000,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematica Bohemica","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.21136/mb.2021.0181-20","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
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Abstract
In this paper some results on direct summands of Goldie extending elements are studied in a modular lattice. An element a of a lattice L with 0 is said to be a Goldie extending element if and only if for every b 6 a there exists a direct summand c of a such that b ∧ c is essential in both b and c. Some characterizations of decomposition of a Goldie extending element in a modular lattice are obtained.
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