{"title":"ON NILPOTENCY OF GRADED ASSOCIATIVE ALGEBRAS","authors":"A. Chanyshev","doi":"10.1070/SM1992V071N02ABEH001402","DOIUrl":null,"url":null,"abstract":"It is proved that an associative PI-algebra over a field of characteristic zero that is graded by an arbitrary semigroup and that satisfies the relation an = 0 for all homogeneous elements and is generated by a finite number of its homogeneous components is nilpotent. This generalizes a well-known theorem of M. Nagata.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"54 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1992-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematics of The Ussr-sbornik","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1070/SM1992V071N02ABEH001402","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 1
Abstract
It is proved that an associative PI-algebra over a field of characteristic zero that is graded by an arbitrary semigroup and that satisfies the relation an = 0 for all homogeneous elements and is generated by a finite number of its homogeneous components is nilpotent. This generalizes a well-known theorem of M. Nagata.
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