{"title":"在有限稳定定义域上","authors":"Stefania Gabelli, M. Roitman","doi":"10.1216/jca.2020.12.179","DOIUrl":null,"url":null,"abstract":"Among other results, we prove the following: (1) A locally Archimedean stable domain satisfies accp. (2) A stable domain R is Archimedean if and only if every nonunit of R belongs to a height-one prime ideal of R′ (this result is related to Ohm’s Theorem for Prüfer domains). (3) An Archimedean stable domain R is one-dimensional if and only if R′ is equidimensional (generally, an Archimedean stable local domain is not necessarily onedimensional). (4) An Archimedean finitely stable semilocal domain with stable maximal ideals is locally Archimedean, but generally, neither Archimedean stable domains, nor Archimedean semilocal domains are necessarily locally Archimedean.","PeriodicalId":49037,"journal":{"name":"Journal of Commutative Algebra","volume":"33 1","pages":""},"PeriodicalIF":0.3000,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"On finitely stable domains, II\",\"authors\":\"Stefania Gabelli, M. Roitman\",\"doi\":\"10.1216/jca.2020.12.179\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Among other results, we prove the following: (1) A locally Archimedean stable domain satisfies accp. (2) A stable domain R is Archimedean if and only if every nonunit of R belongs to a height-one prime ideal of R′ (this result is related to Ohm’s Theorem for Prüfer domains). (3) An Archimedean stable domain R is one-dimensional if and only if R′ is equidimensional (generally, an Archimedean stable local domain is not necessarily onedimensional). (4) An Archimedean finitely stable semilocal domain with stable maximal ideals is locally Archimedean, but generally, neither Archimedean stable domains, nor Archimedean semilocal domains are necessarily locally Archimedean.\",\"PeriodicalId\":49037,\"journal\":{\"name\":\"Journal of Commutative Algebra\",\"volume\":\"33 1\",\"pages\":\"\"},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2020-06-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Commutative Algebra\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1216/jca.2020.12.179\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Commutative Algebra","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1216/jca.2020.12.179","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
Among other results, we prove the following: (1) A locally Archimedean stable domain satisfies accp. (2) A stable domain R is Archimedean if and only if every nonunit of R belongs to a height-one prime ideal of R′ (this result is related to Ohm’s Theorem for Prüfer domains). (3) An Archimedean stable domain R is one-dimensional if and only if R′ is equidimensional (generally, an Archimedean stable local domain is not necessarily onedimensional). (4) An Archimedean finitely stable semilocal domain with stable maximal ideals is locally Archimedean, but generally, neither Archimedean stable domains, nor Archimedean semilocal domains are necessarily locally Archimedean.
期刊介绍:
Journal of Commutative Algebra publishes significant results in the area of commutative algebra and closely related fields including algebraic number theory, algebraic geometry, representation theory, semigroups and monoids.
The journal also publishes substantial expository/survey papers as well as conference proceedings. Any person interested in editing such a proceeding should contact one of the managing editors.