{"title":"半环是主左k基的并","authors":"T. K. Mondal","doi":"10.56415/qrs.v30.12","DOIUrl":null,"url":null,"abstract":"Here we study the principal left k-radicals of a semiring with semilattice additive reduct and characterize the semirings which are disjoint union of principal left k-radicals via the −→ transitive closure l ∞ of the relation −→l on a semiring S, given by for a, b ∈ S, a −→l b ⇔ bn ∈ Sa for some n ∈ N.","PeriodicalId":38681,"journal":{"name":"Quasigroups and Related Systems","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2022-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Semirings which are union of principal left k-radicals\",\"authors\":\"T. K. Mondal\",\"doi\":\"10.56415/qrs.v30.12\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Here we study the principal left k-radicals of a semiring with semilattice additive reduct and characterize the semirings which are disjoint union of principal left k-radicals via the −→ transitive closure l ∞ of the relation −→l on a semiring S, given by for a, b ∈ S, a −→l b ⇔ bn ∈ Sa for some n ∈ N.\",\"PeriodicalId\":38681,\"journal\":{\"name\":\"Quasigroups and Related Systems\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-05-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Quasigroups and Related Systems\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.56415/qrs.v30.12\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Quasigroups and Related Systems","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.56415/qrs.v30.12","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: 0
摘要
本文研究了具有半格加性约的半环的主左k根,并利用半环S上的关系-→l的-→传递闭包l∞刻画了主左k根不相交并的半环,给出了对于a, b∈S,对于n∈n, a -→l b⇔bn∈Sa。
Semirings which are union of principal left k-radicals
Here we study the principal left k-radicals of a semiring with semilattice additive reduct and characterize the semirings which are disjoint union of principal left k-radicals via the −→ transitive closure l ∞ of the relation −→l on a semiring S, given by for a, b ∈ S, a −→l b ⇔ bn ∈ Sa for some n ∈ N.