Cite this article as:

Antonov S. Y., Antonova A. V. To Chang Theorem. Izv. Saratov Univ. (N. S.), Ser. Math. Mech. Inform., 2015, vol. 15, iss. 3, pp. 247-250. DOI: https://doi.org/10.18500/1816-9791-2015-15-3-247-251

Language: 
Russian
Heading: 
Mathematics
UDC: 
512

To Chang Theorem

Authors: 
Antonov Stepan Yuryevich, Kazan State Power Engineering University, 51, Krasnosel’skaya st., 420066, Kazan, Russia , antonovst-vm@rambler.ru
Antonova Alina Vladimirovna, Kazan State Power Engineering University, 51, Krasnosel’skaya st., 420066, Kazan, Russia , antonovakazan@rambler.ru
Abstract: 

Multilinear polynomials H (¯x, ¯y) and R(¯x, ¯y), the sum of which is the Chang polynomial F(¯x, ¯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−(¯x). In particular it has been shown that the double Capelli polynomial of add degree C2m−1(¯x, ¯y) is also a consequence of the polynomial S−m(¯x, ¯y). The minimal degree of the polynomial C2m−1(¯x, ¯y) in which it is a polynomial identity of matrix algebraMn(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
DOI: 
https://doi.org/10.18500/1816-9791-2015-15-3-247-251
References
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