Identities of sum of two PI-algebras in the case of positive characteristic-Reference-Cited by-同舟云学术

Identities of sum of two PI-algebras in the case of positive characteristic

Published:2015-12 Issue:08 Volume:25 Page:1265-1273
ISSN:0218-1967
Container-title:International Journal of Algebra and Computation
language:en
Short-container-title:Int. J. Algebra Comput.

Author:

Kaygorodov Ivan¹,Lopatin Artem A.²³,Popov Yury⁴

Affiliation:

1. Universidade Federal do ABC, CMCC, Campus Santo André, Avenida dos Estados 5001, Santo André, SP, CEP 09210-580, Brazil

2. Sobolev Institute of Mathematics, Omsk Branch, SB RAS, Pevtsova street, 13, 644043, Omsk, Russia

3. Universidade Estadual de Campinas, IMECC, Rua Sérgio Buarque de Holanda, 651 Distr. Barão Geraldo, Campinas SP, CEP 13083-859, Brazil

4. Sobolev Institute of Mathematics, SB RAS, pr. akad. Koptyga 4, 630090, Novosibirsk, Russia

Abstract

We consider the following question posted by Beidar and Mikhalev in 1995 for an associative ring [Formula: see text]: is it true that if the subrings [Formula: see text] and [Formula: see text] satisfy polynomial identities, then [Formula: see text] also satisfies a polynomial identity? Over a field of positive characteristic we establish new conditions on [Formula: see text] and [Formula: see text] that guarantee a positive answer to the question. We find upper and low bounds on the degrees of identities of [Formula: see text].

Publisher

World Scientific Pub Co Pte Lt

Subject

General Mathematics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S021819671550040X

Reference19 articles.

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4. The standard identity in characteristicp a conjecture of I.B. Volichenko

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1. A ring which is a sum of two PI subrings is always a PI ring;Israel Journal of Mathematics;2017-07-26