{"title":"具有半净镍性能的合金环","authors":"Vijay. Venkatachalam, Selvaraj Chelliah","doi":"10.56947/gjom.v14i1.1093","DOIUrl":null,"url":null,"abstract":"An element in a ring R is said to be semi nil-clean if it is a sum of nilpotent and periodic elements in R. An element in a ring R is said to be semiclean if it is a sum of unit and periodic elements in R. A ring R is said to be semi nil-clean (resp., semiclean) if every element in R is semi nil-clean (resp., semiclean). We discuss some basic properties of semi nil-clean ring and we also study the concepts of semi nil-clean and semiclean properties in various context of commutative rings such as amalgamations and the ring of polynomials R[x] of a ring R.","PeriodicalId":421614,"journal":{"name":"Gulf Journal of Mathematics","volume":"304 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2023-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Amalgamated rings with semi nil-clean properties\",\"authors\":\"Vijay. Venkatachalam, Selvaraj Chelliah\",\"doi\":\"10.56947/gjom.v14i1.1093\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"An element in a ring R is said to be semi nil-clean if it is a sum of nilpotent and periodic elements in R. An element in a ring R is said to be semiclean if it is a sum of unit and periodic elements in R. A ring R is said to be semi nil-clean (resp., semiclean) if every element in R is semi nil-clean (resp., semiclean). We discuss some basic properties of semi nil-clean ring and we also study the concepts of semi nil-clean and semiclean properties in various context of commutative rings such as amalgamations and the ring of polynomials R[x] of a ring R.\",\"PeriodicalId\":421614,\"journal\":{\"name\":\"Gulf Journal of Mathematics\",\"volume\":\"304 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-01-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Gulf Journal of Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.56947/gjom.v14i1.1093\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Gulf Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.56947/gjom.v14i1.1093","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
An element in a ring R is said to be semi nil-clean if it is a sum of nilpotent and periodic elements in R. An element in a ring R is said to be semiclean if it is a sum of unit and periodic elements in R. A ring R is said to be semi nil-clean (resp., semiclean) if every element in R is semi nil-clean (resp., semiclean). We discuss some basic properties of semi nil-clean ring and we also study the concepts of semi nil-clean and semiclean properties in various context of commutative rings such as amalgamations and the ring of polynomials R[x] of a ring R.