{"title":"非交换环的弱素和弱完全素理想","authors":"N. Groenewald","doi":"10.24330/ieja.768127","DOIUrl":null,"url":null,"abstract":"Anderson-Smith studied weakly prime ideals for a commutative ring with identity. Hirano, Poon and Tsutsui studied the structure of a ring in which every ideal is weakly prime for rings, not necessarily commutative. In this note we give some more properties of weakly prime ideals in noncommutative rings. We introduce the notion of a weakly prime radical of an ideal. We initiate the study of weakly completely prime ideals and investigate rings for which every proper ideal is weakly completely prime.","PeriodicalId":43749,"journal":{"name":"International Electronic Journal of Algebra","volume":" ","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2020-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"7","resultStr":"{\"title\":\"WEAKLY PRIME AND WEAKLY COMPLETELY PRIME IDEALS OF NONCOMMUTATIVE RINGS\",\"authors\":\"N. Groenewald\",\"doi\":\"10.24330/ieja.768127\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Anderson-Smith studied weakly prime ideals for a commutative ring with identity. Hirano, Poon and Tsutsui studied the structure of a ring in which every ideal is weakly prime for rings, not necessarily commutative. In this note we give some more properties of weakly prime ideals in noncommutative rings. We introduce the notion of a weakly prime radical of an ideal. We initiate the study of weakly completely prime ideals and investigate rings for which every proper ideal is weakly completely prime.\",\"PeriodicalId\":43749,\"journal\":{\"name\":\"International Electronic Journal of Algebra\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2020-07-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"7\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Electronic Journal of Algebra\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.24330/ieja.768127\",\"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.768127","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
WEAKLY PRIME AND WEAKLY COMPLETELY PRIME IDEALS OF NONCOMMUTATIVE RINGS
Anderson-Smith studied weakly prime ideals for a commutative ring with identity. Hirano, Poon and Tsutsui studied the structure of a ring in which every ideal is weakly prime for rings, not necessarily commutative. In this note we give some more properties of weakly prime ideals in noncommutative rings. We introduce the notion of a weakly prime radical of an ideal. We initiate the study of weakly completely prime ideals and investigate rings for which every proper ideal is weakly completely prime.
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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