{"title":"2-超幂零Mal’cev代数。","authors":"Nebojša Mudrinski","doi":"10.1007/s00605-013-0541-y","DOIUrl":null,"url":null,"abstract":"<p><p>In this note we prove that a Mal'cev algebra is 2-supernilpotent ([1, 1, 1] = 0) if and only if it is polynomially equivalent to a special expanded group. This generalizes Gumm's result that a Mal'cev algebra is abelian if and only if it is polynomially equivalent to a module over a ring.</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2013-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s00605-013-0541-y","citationCount":"2","resultStr":"{\"title\":\"2-Supernilpotent Mal'cev algebras.\",\"authors\":\"Nebojša Mudrinski\",\"doi\":\"10.1007/s00605-013-0541-y\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p><p>In this note we prove that a Mal'cev algebra is 2-supernilpotent ([1, 1, 1] = 0) if and only if it is polynomially equivalent to a special expanded group. This generalizes Gumm's result that a Mal'cev algebra is abelian if and only if it is polynomially equivalent to a module over a ring.</p>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2013-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1007/s00605-013-0541-y\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s00605-013-0541-y\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"2013/8/31 0:00:00\",\"PubModel\":\"Epub\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00605-013-0541-y","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2013/8/31 0:00:00","PubModel":"Epub","JCR":"","JCRName":"","Score":null,"Total":0}
In this note we prove that a Mal'cev algebra is 2-supernilpotent ([1, 1, 1] = 0) if and only if it is polynomially equivalent to a special expanded group. This generalizes Gumm's result that a Mal'cev algebra is abelian if and only if it is polynomially equivalent to a module over a ring.
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