Fitriana Hasnani, Meryta Febrilian Fatimah, N. P. Puspita
{"title":"The notions of irreducible ideals of the endomorphism ring on the category of rings and the category of modules","authors":"Fitriana Hasnani, Meryta Febrilian Fatimah, N. P. Puspita","doi":"10.24042/ajpm.v13i1.11139","DOIUrl":null,"url":null,"abstract":"Let R commutative ring with multiplicative identity, and M is an R-module. An ideal I of R is irreducible if the intersection of every two ideals of R equals I, then one of them is I itself. Module theory is also known as an irreducible submodule, from the concept of an irreducible ideal in the ring. The set of R - module homomorphisms from M to itself is denoted by EndR(M). It is called a module endomorphism M of ring R. The set EndR(M) is also a ring with an addition operation and composition function. This paper showed the sufficient condition of an irreducible ideal on the ring of EndR(R) and EndR(M)","PeriodicalId":385020,"journal":{"name":"Al-Jabar : Jurnal Pendidikan Matematika","volume":"30 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2022-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Al-Jabar : Jurnal Pendidikan Matematika","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.24042/ajpm.v13i1.11139","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 1
Abstract
Let R commutative ring with multiplicative identity, and M is an R-module. An ideal I of R is irreducible if the intersection of every two ideals of R equals I, then one of them is I itself. Module theory is also known as an irreducible submodule, from the concept of an irreducible ideal in the ring. The set of R - module homomorphisms from M to itself is denoted by EndR(M). It is called a module endomorphism M of ring R. The set EndR(M) is also a ring with an addition operation and composition function. This paper showed the sufficient condition of an irreducible ideal on the ring of EndR(R) and EndR(M)