{"title":"推导等价下广义雷诺理想的不变性","authors":"A. Zimmermann","doi":"10.3318/PRIA.2007.107.1.1","DOIUrl":null,"url":null,"abstract":"For any algebraically closed field $k$ of positive characteristic $p$ and any non negative integer $n$ K\\\"ulshammer defined ideals $T\\_nA^\\perp$ of the centre of a symmetric $k$-algebra $A$. We show that for derived equivalent algebras $A$ and $B$ there is an isomorphism of the centres of $A$ and $B$ mapping $T\\_nA^\\perp$ to $T\\_nB^\\perp$ for all $n$. Recently H\\'ethelyi, Horv\\'ath, K\\\"ulshammer and Murray showed that this holds for Morita equivalent algebras.","PeriodicalId":434988,"journal":{"name":"Mathematical Proceedings of the Royal Irish Academy","volume":"19 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2005-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"20","resultStr":"{\"title\":\"INVARIANCE OF GENERALISED REYNOLDS IDEALS UNDER DERIVED EQUIVALENCES\",\"authors\":\"A. Zimmermann\",\"doi\":\"10.3318/PRIA.2007.107.1.1\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"For any algebraically closed field $k$ of positive characteristic $p$ and any non negative integer $n$ K\\\\\\\"ulshammer defined ideals $T\\\\_nA^\\\\perp$ of the centre of a symmetric $k$-algebra $A$. We show that for derived equivalent algebras $A$ and $B$ there is an isomorphism of the centres of $A$ and $B$ mapping $T\\\\_nA^\\\\perp$ to $T\\\\_nB^\\\\perp$ for all $n$. Recently H\\\\'ethelyi, Horv\\\\'ath, K\\\\\\\"ulshammer and Murray showed that this holds for Morita equivalent algebras.\",\"PeriodicalId\":434988,\"journal\":{\"name\":\"Mathematical Proceedings of the Royal Irish Academy\",\"volume\":\"19 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2005-09-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"20\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematical Proceedings of the Royal Irish Academy\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.3318/PRIA.2007.107.1.1\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Proceedings of the Royal Irish Academy","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3318/PRIA.2007.107.1.1","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
INVARIANCE OF GENERALISED REYNOLDS IDEALS UNDER DERIVED EQUIVALENCES
For any algebraically closed field $k$ of positive characteristic $p$ and any non negative integer $n$ K\"ulshammer defined ideals $T\_nA^\perp$ of the centre of a symmetric $k$-algebra $A$. We show that for derived equivalent algebras $A$ and $B$ there is an isomorphism of the centres of $A$ and $B$ mapping $T\_nA^\perp$ to $T\_nB^\perp$ for all $n$. Recently H\'ethelyi, Horv\'ath, K\"ulshammer and Murray showed that this holds for Morita equivalent algebras.