{"title":"A note on 2-prime and n-weakly 2-prime ideals of semirings","authors":"Biswaranjan Khanra, M. Mandal, S. Das","doi":"10.56415/qrs.v30.20","DOIUrl":null,"url":null,"abstract":"We introduce and study the concepts of 2-prime and n-weakly 2-prime (resp. weakly 2-prime) ideals in a commutative semiring. We prove that an integral semidomain S is a valuation semiring if and only if every proper ideal of S is 2-prime and in a principal ideal semidomain the concepts of primary, quasi-primary and 2-prime ideals coincide. We characterize semirings where 2-prime ideals are prime and also characterize semirings where every proper ideal is n-weakly 2-prime (resp. weakly 2-prime)","PeriodicalId":38681,"journal":{"name":"Quasigroups and Related Systems","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2023-04-01","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.v30.20","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
Abstract
We introduce and study the concepts of 2-prime and n-weakly 2-prime (resp. weakly 2-prime) ideals in a commutative semiring. We prove that an integral semidomain S is a valuation semiring if and only if every proper ideal of S is 2-prime and in a principal ideal semidomain the concepts of primary, quasi-primary and 2-prime ideals coincide. We characterize semirings where 2-prime ideals are prime and also characterize semirings where every proper ideal is n-weakly 2-prime (resp. weakly 2-prime)