{"title":"模格中Goldie扩展元素的直接求和","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":"{\"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}","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}
Direct summands of Goldie extending elements in modular lattices
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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