{"title":"交换群代数的 Krull-Remak-Schmidt 分解","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":"{\"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}","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}
The Krull-Remak-Schmidt decomposition of commutative group algebras
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.