{"title":"环扩张上星运算的一些性质","authors":"Lokendra Paudel, S. Tchamna","doi":"10.24330/IEJA.969592","DOIUrl":null,"url":null,"abstract":"Let ? be a star operation on a ring extension R ⊆ S. A ring extension R ⊆ S is called Prüfer star-multiplication extension (P?ME) if (R[m],m[m]) is a Manis pair in S for every ?-maximal ideal m of R [L. Paudel and S. Tchamna, A study of linked star operations, to appear in Bull. Korean Math. Soc., Definition 3.1]. We establish some results on star operations, and we study P?ME in pullback diagrams of type . We show that, for a maximal ideal m of R, the extension R[m] ⊆ S is Manis if and only if R[X][mR[X]] ⊆ S[X] is a Manis extension. Mathematics Subject Classification (2020): 13A15, 13A18, 13B02","PeriodicalId":43749,"journal":{"name":"International Electronic Journal of Algebra","volume":" ","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2021-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"SOME PROPERTIES OF STAR OPERATIONS ON RING EXTENSIONS\",\"authors\":\"Lokendra Paudel, S. Tchamna\",\"doi\":\"10.24330/IEJA.969592\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let ? be a star operation on a ring extension R ⊆ S. A ring extension R ⊆ S is called Prüfer star-multiplication extension (P?ME) if (R[m],m[m]) is a Manis pair in S for every ?-maximal ideal m of R [L. Paudel and S. Tchamna, A study of linked star operations, to appear in Bull. Korean Math. Soc., Definition 3.1]. We establish some results on star operations, and we study P?ME in pullback diagrams of type . We show that, for a maximal ideal m of R, the extension R[m] ⊆ S is Manis if and only if R[X][mR[X]] ⊆ S[X] is a Manis extension. Mathematics Subject Classification (2020): 13A15, 13A18, 13B02\",\"PeriodicalId\":43749,\"journal\":{\"name\":\"International Electronic Journal of Algebra\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2021-07-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Electronic Journal of Algebra\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.24330/IEJA.969592\",\"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":"International Electronic Journal of Algebra","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.24330/IEJA.969592","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
SOME PROPERTIES OF STAR OPERATIONS ON RING EXTENSIONS
Let ? be a star operation on a ring extension R ⊆ S. A ring extension R ⊆ S is called Prüfer star-multiplication extension (P?ME) if (R[m],m[m]) is a Manis pair in S for every ?-maximal ideal m of R [L. Paudel and S. Tchamna, A study of linked star operations, to appear in Bull. Korean Math. Soc., Definition 3.1]. We establish some results on star operations, and we study P?ME in pullback diagrams of type . We show that, for a maximal ideal m of R, the extension R[m] ⊆ S is Manis if and only if R[X][mR[X]] ⊆ S[X] is a Manis extension. Mathematics Subject Classification (2020): 13A15, 13A18, 13B02
期刊介绍：
The International Electronic Journal of Algebra is published twice a year. IEJA is reviewed by Mathematical Reviews, MathSciNet, Zentralblatt MATH, Current Mathematical Publications. IEJA seeks previously unpublished papers that contain: Module theory Ring theory Group theory Algebras Comodules Corings Coalgebras Representation theory Number theory.
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