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

Author(s)

Kaygorodov, Ivan ^[1] ; Lopatin, Artem A. ^{[2, 3]} ; Popov, Yury ^[4]

Affiliation

^[1] Univ Fed ABC, CMCC, Campus Santo Andre, Ave Estados 5001, BR-09210580 Santo Andre, SP - Brazil

^[2] Univ Estadual Campinas, IMECC, BR-13083859 Campinas, SP - Brazil

^[3] SB RAS, Omsk Branch, Sobolev Inst Math, Omsk 644043 - Russia

^[4] SB RAS, Sobolev Inst Math, Novosibirsk 630090 - Russia

• Document type: Journal article
• Source: INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION; v. 25, n. 8, p. 1265-1273, DEC 2015.
• Web of Science Citations: 1

Abstract

We consider the following question posted by Beidar and Mikhalev in 1995 for an associative ring R = R-1 + R-2: is it true that if the subrings R-1 and R-2 satisfy polynomial identities, then R also satisfies a polynomial identity? Over a field of positive characteristic we establish new conditions on R-1 and R-2 that guarantee a positive answer to the question. We find upper and low bounds on the degrees of identities of R. (AU)

• FAPESP's process: 13/15539-2 - Identities for the algebra of matrices over a field of arbitrary characteristic
• Grantee: Artem Lopatin
• Support Opportunities: Regular Research Grants