A characterization of minimal varieties of Zp-graded PI algebras

[摘要] Let F be a field of characteristic zero and p a prime. In the present paper it is proved that a variety of Z(p)-graded associative PI F-algebras of finite basic rank is minimal of fixed Z(p)-exponent d if, and only if, it is generated by an upper block triangular matrix algebra UTz(p) (A(1), ..., A(m)) equipped with a suitable elementary Z(p)-grading, whose diagonal blocks are isomorphic to Z(p)-graded simple algebras A(1), ..., A(m) satisfying dim(F)(A(1) circle plus ... circle plus A(m)) = d. (C) 2019 Elsevier Inc. All rights reserved.

[发布日期] 2019-12-01

[关键词] Graded algebras;Graded polynomial identities;G-exponent;Minimal varieties;Upper block triangular matrix algebras