On the identities of the Grassmann algebras in characteristic p > 0

dc.creatorGiambruno, A
dc.creatorKoshlukov, P
dc.date2001
dc.date2014-11-14T02:30:37Z
dc.date2015-11-26T16:03:55Z
dc.date2014-11-14T02:30:37Z
dc.date2015-11-26T16:03:55Z
dc.date.accessioned2018-03-28T22:53:07Z
dc.date.available2018-03-28T22:53:07Z
dc.identifierIsrael Journal Of Mathematics. Magnes Press, v. 122, n. 305, n. 316, 2001.
dc.identifier0021-2172
dc.identifierWOS:000169028000018
dc.identifier10.1007/BF02809905
dc.identifierhttp://www.repositorio.unicamp.br/jspui/handle/REPOSIP/68687
dc.identifierhttp://www.repositorio.unicamp.br/handle/REPOSIP/68687
dc.identifierhttp://repositorio.unicamp.br/jspui/handle/REPOSIP/68687
dc.identifier.urihttp://repositorioslatinoamericanos.uchile.cl/handle/2250/1265379
dc.descriptionIn this note we exhibit bases of the polynomial identities satisfied by the Grassmann algebras over a field of positive characteristic. This allows us to answer the following question of Kemer: Does the infinite dimensional Grassmann algebra with 1, over an infinite field K of characteristic 3, satisfy all identities of the algebra M-2(K) of all 2 x 2 matrices over K? We give a negative answer to this question. Further, we show that certain finite dimensional Grassmann algebras do give a positive answer to Kemer's question. All this allows us to obtain some information about the identities satisfied by the algebra M-2(K) over an infinite field K of positive odd characteristic, and to conjecture bases of the identities of M-2(K).
dc.description122
dc.description305
dc.description316
dc.languageen
dc.publisherMagnes Press
dc.publisherJerusalem
dc.publisherIsrael
dc.relationIsrael Journal Of Mathematics
dc.relationIsr. J. Math.
dc.rightsfechado
dc.sourceWeb of Science
dc.subjectNilpotent Lie-algebras
dc.subjectRepresentations
dc.titleOn the identities of the Grassmann algebras in characteristic p > 0
dc.typeArtículos de revistas


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