For citation:
Antonov S. Y., Antonova A. V. To Chang Theorem. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2015, vol. 15, iss. 3, pp. 247-250. DOI: 10.18500/1816-9791-2015-15-3-247-251, EDN: UKIVCX
To Chang Theorem
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.
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