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| A SORT OF POLYNOMIAL IDENTITIES OF $\[{M_n}(F)\]$ WITH CHAR $\[F \ne 0\]$ |
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Citation： |
Chang Qing.A SORT OF POLYNOMIAL IDENTITIES OF $\[{M_n}(F)\]$ WITH CHAR $\[F \ne 0\]$[J].Chinese Annals of Mathematics B,1988,9(2):161~166 |
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Net amount： 729 |
Authors： |
Chang Qing; |
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| Abstract： |
Let $F$ denote a field, finite or infinite, with characteristic $\[p \ne 0\]$. In this paper, the
author obtains the following result: The symmetric polynomial on $t$ letters
$$\[{S_{sym(t)}}({x_1},{x_2}, \cdots ,{x_t}) = \sum\limits_{x \in sym(t)} {{X_{\pi 1}}{X_{\pi 2}} \cdots {X_{\pi t}}} \]$$
is a polynomial identity of $\[{M_n}(F)\]$ when $\[t \ge pn\]$, and this is sharp in the sense that if $\[t \le pn - 1\]$,it is not a polynomial identity of $\[{M_n}(F)\]$. |
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