It has been recently proved that a variety of associative PI-superalgebras with graded involution of finite basic rank over a field of characteristic zero is minimal of fixed ⁎-graded exponent if, and only if, it is generated by a subalgebra of an upper block triangular matrix algebra, A:=UT_{Z_2,*}(A_1, ...., A_k), equipped with a suitable elementary Z2-grading and graded involution. Here we give necessary and sufficient conditions so that Id_{Z_2,⁎}(A) factorizes in the product of the ideals of ⁎-graded polynomial identities of its ⁎-graded simple components Ai.
On the factorability of the ideal of ⁎-graded polynomial identities of minimal varieties of PI ⁎-superalgebras
Di Vincenzo O. M.;
2022-01-01
Abstract
It has been recently proved that a variety of associative PI-superalgebras with graded involution of finite basic rank over a field of characteristic zero is minimal of fixed ⁎-graded exponent if, and only if, it is generated by a subalgebra of an upper block triangular matrix algebra, A:=UT_{Z_2,*}(A_1, ...., A_k), equipped with a suitable elementary Z2-grading and graded involution. Here we give necessary and sufficient conditions so that Id_{Z_2,⁎}(A) factorizes in the product of the ideals of ⁎-graded polynomial identities of its ⁎-graded simple components Ai.File in questo prodotto:
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