{"title":"The Krull-Remak-Schmidt decomposition of commutative group algebras","authors":"Robert Christian Subroto","doi":"arxiv-2408.14665","DOIUrl":null,"url":null,"abstract":"We provide the Krull-Remak-Schmidt decomposition of group algebras of the\nform $k[G]$ where $k$ is a field, which includes fields with prime\ncharacteristic, and $G$ a finite abelian group. We achieved this by studying\nthe geometric equivalence of $k[G]$ which we call circulant coordinate rings.","PeriodicalId":501136,"journal":{"name":"arXiv - MATH - Rings and Algebras","volume":"74 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Rings and Algebras","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2408.14665","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We provide the Krull-Remak-Schmidt decomposition of group algebras of the
form $k[G]$ where $k$ is a field, which includes fields with prime
characteristic, and $G$ a finite abelian group. We achieved this by studying
the geometric equivalence of $k[G]$ which we call circulant coordinate rings.
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