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 dimF(A_1⊕⋯⊕A_m)=d.
A characterization of minimal varieties of Zp-graded PI algebras
Di Vincenzo Mario;
2019-01-01
Abstract
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 dimF(A_1⊕⋯⊕A_m)=d.File in questo prodotto:
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