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This article is cited in 4 scientific papers (total in 4 papers)
Mathematics
To Chang theorem
S. Yu. Antonov, A. V. Antonova Kazan State Power Engineering University, 51, Krasnosel’skaya st., 420066, Kazan, Russia
Abstract:
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.
Key words:
$T$-ideal, standard polynomial, Capelli polynomial.
Citation:
S. Yu. Antonov, A. V. Antonova, “To Chang theorem”, Izv. Saratov Univ. Math. Mech. Inform., 15:3 (2015), 247–251
Linking options:
https://www.mathnet.ru/eng/isu589 https://www.mathnet.ru/eng/isu/v15/i3/p247
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Abstract page: | 275 | Full-text PDF : | 84 | References: | 61 |
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