{"title":"关于分级-格尔芬德交换环","authors":"Mohamed Aqalmoun","doi":"10.1142/s0219498825501695","DOIUrl":null,"url":null,"abstract":"This paper deals with the graded commutative rings in which every graded prime ideal is contained in a unique graded-maximal ideal called graded-Gelfand ring. The purpose is to establish some topological and algebraic characterizations of these rings, one of which is the algebraic analogue of Urysohn’s lemma. Finally, we look at a special class of those graded rings called graded-ordered rings which can be viewed as graded rings with a Gelfand strong property.","PeriodicalId":508127,"journal":{"name":"Journal of Algebra and Its Applications","volume":"54 5-6","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the graded-Gelfand commutative rings\",\"authors\":\"Mohamed Aqalmoun\",\"doi\":\"10.1142/s0219498825501695\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper deals with the graded commutative rings in which every graded prime ideal is contained in a unique graded-maximal ideal called graded-Gelfand ring. The purpose is to establish some topological and algebraic characterizations of these rings, one of which is the algebraic analogue of Urysohn’s lemma. Finally, we look at a special class of those graded rings called graded-ordered rings which can be viewed as graded rings with a Gelfand strong property.\",\"PeriodicalId\":508127,\"journal\":{\"name\":\"Journal of Algebra and Its Applications\",\"volume\":\"54 5-6\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-02-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Algebra and Its Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1142/s0219498825501695\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Algebra and Its Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1142/s0219498825501695","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
This paper deals with the graded commutative rings in which every graded prime ideal is contained in a unique graded-maximal ideal called graded-Gelfand ring. The purpose is to establish some topological and algebraic characterizations of these rings, one of which is the algebraic analogue of Urysohn’s lemma. Finally, we look at a special class of those graded rings called graded-ordered rings which can be viewed as graded rings with a Gelfand strong property.
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