This article is cited in 2 papers

An analog of the Amitsur–Levitzki theorem for matrix superalgebras

L. M. Samoĭlov

Ulyanovsk State University, Faculty of Mathematics and Information Technologies, Ulyanovsk

Abstract: We construct a polynomial identity of degree $2(nk+n+k)-\min\{n,k\}$ for the matrix superalgebra $M_{n,k}$ over a field of characteristic zero. The conjecture is formulated that $M_{n,k}$ lacks any identities of lower degree.

Keywords: matrix superalgebra, polynomial identity, trace identity.

UDC: 512.552.4

Received: 19.02.2009

 English version: Siberian Mathematical Journal, 2010, 51:3, 491–495

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