Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)


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

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
11.09.2015
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Russian
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512
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UKIVCX

To Chang Theorem

Autors: 
Antonova Alina Vladimirovna, Kazan State Power Engineering University, Russia
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.

References: 
  1. Chang Q. Some consequences of the standard polynomial // Proc. Amer. Math. Soc. 1988. Vol. 104, № 3. P. 707–710.  
  2. Pierce R. Associative Algebras. N.Y. : SpringerVerlag, 1982. 542 p.
  3. Amitsur S. A., Levitzki J. Minimal identities for algebras // Proc. Amer. Math. Soc. 1950. Vol. 1, № 4. P. 449–463.
  4. Антонов С. Ю. Наименьшая степень тождеств подпространства M(m,k) 1 (F) матричной супералгебры M(m,k)(F) // Изв. вузов. Математика. 2012. № 11. С. 3–19.
  5. Domokos M. A generalization of a theorem of Chang // Commun. Algebra. 1995. Vol. 23, № 12. P. 4333–4342.
Received: 
23.04.2015
Accepted: 
29.08.2015
Published: 
30.09.2015