To Chang theorem

S. Yu. Antonov ; A. V. Antonova

Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 15 (2015) no. 3, pp. 247-251

Résumé

Multilinear polynomials $\mathcal{H}(\bar x, \bar y)$ and $\mathcal{R}(\bar x, \bar y)$, the sum of which is the Chang polynomial $\mathcal{F}(\bar x, \bar y)$ have been introduced in this paper. It has been proved by mathematical induction method that each of them is a consequence of the standard polynomial $S^-(\bar x)$. In particular it has been shown that the double Capelli polynomial of add degree $C_{2m-1}(\bar x, \bar y)$ is also a consequence of the polynomial $S_m^-(\bar x, \bar y)$. The minimal degree of the polynomial $C_{2m-1}(\bar x, \bar y)$ in which it is a polynomial identity of matrix algebra $M_n(F)$ has been also found in the paper. The results obtained are the transfer of Chang's results over to the double Capelli polynomials of add degree.