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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)


Multilinear identities of the matrix ring

Author: Uri Leron
Journal: Trans. Amer. Math. Soc. 183 (1973), 175-202
MSC: Primary 16A42
MathSciNet review: 0332873
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Abstract: Let V be a vector space over a field F of zero characteristic, which is acted upon by the symmetric group. Systems of generators for V are constructed, which have special symmetry and skew symmetry properties. This is applied to prove that every multilinear polynomial identity of degree $ 2n + 1$ which holds in the matrix ring $ {F_n}(n > 2)$ is a consequence of the standard identity $ {s_{2n}}$. The notions of rigid and semirigid sequences of matrices are defined and treated.

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PII: S 0002-9947(1973)0332873-3
Keywords: Matrix ring, multilinear polynomial, standard identity, rigid and semirigid sequences
Article copyright: © Copyright 1973 American Mathematical Society