A sort of polynomial identities of \(M_ n(F)\) with char F\(\neq 0\) (Q1110636)
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scientific article; zbMATH DE number 4073211
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A sort of polynomial identities of \(M_ n(F)\) with char F\(\neq 0\) |
scientific article; zbMATH DE number 4073211 |
Statements
A sort of polynomial identities of \(M_ n(F)\) with char F\(\neq 0\) (English)
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1988
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Let F be a field of characteristic \(p>0\), and let \(S_ t\) denote the symmetric group on t letters. It is shown that \(S(x_ 1,x_ 2,...,x_ t)=\sum_{\pi \in S_ t}x_{\pi (1)}x_{\pi (2)}...x_{\pi (t)}\) is a polynomial identity of the matrix algebra \(M_ n(F)\) if \(t\geq pn\), and it is not an identity of \(M_ n(F)\) if \(t<pn\).
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symmetric group
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polynomial identity
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matrix algebra
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