{"title":"半正规c -一元群的一个性质。","authors":"Alfred Geroldinger, Qinghai Zhong","doi":"10.1007/s40574-019-00194-9","DOIUrl":null,"url":null,"abstract":"<p><p>It is well-known that a C-monoid is completely integrally closed if and only if its reduced class semigroup is a group and if this holds, then the C-monoid is a Krull monoid and the reduced class semigroup coincides with the usual class group of Krull monoids. We prove that a C-monoid is seminormal if and only if its reduced class semigroup is a union of groups. Based on this characterization we establish a criterion (in terms of the class semigroup) when seminormal C-monoids are half-factorial.</p>","PeriodicalId":72440,"journal":{"name":"Bollettino della Unione matematica italiana (2008)","volume":"12 4","pages":"583-597"},"PeriodicalIF":0.0000,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40574-019-00194-9","citationCount":"5","resultStr":"{\"title\":\"A characterization of seminormal C-monoids.\",\"authors\":\"Alfred Geroldinger, Qinghai Zhong\",\"doi\":\"10.1007/s40574-019-00194-9\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p><p>It is well-known that a C-monoid is completely integrally closed if and only if its reduced class semigroup is a group and if this holds, then the C-monoid is a Krull monoid and the reduced class semigroup coincides with the usual class group of Krull monoids. We prove that a C-monoid is seminormal if and only if its reduced class semigroup is a union of groups. Based on this characterization we establish a criterion (in terms of the class semigroup) when seminormal C-monoids are half-factorial.</p>\",\"PeriodicalId\":72440,\"journal\":{\"name\":\"Bollettino della Unione matematica italiana (2008)\",\"volume\":\"12 4\",\"pages\":\"583-597\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2019-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1007/s40574-019-00194-9\",\"citationCount\":\"5\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Bollettino della Unione matematica italiana (2008)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1007/s40574-019-00194-9\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"2019/2/9 0:00:00\",\"PubModel\":\"Epub\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Bollettino della Unione matematica italiana (2008)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s40574-019-00194-9","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2019/2/9 0:00:00","PubModel":"Epub","JCR":"","JCRName":"","Score":null,"Total":0}
It is well-known that a C-monoid is completely integrally closed if and only if its reduced class semigroup is a group and if this holds, then the C-monoid is a Krull monoid and the reduced class semigroup coincides with the usual class group of Krull monoids. We prove that a C-monoid is seminormal if and only if its reduced class semigroup is a union of groups. Based on this characterization we establish a criterion (in terms of the class semigroup) when seminormal C-monoids are half-factorial.
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