{"title":"关于分级结合代数的幂零性","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":"{\"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}","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}
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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