On the factorability of the ideal of ⁎-graded polynomial identities of minimal varieties of PI ⁎-superalgebras

It has been recently proved that a variety of associative PI-superalgebras with graded involution finite basic rank over field characteristic zero is minimal fixed ⁎-graded exponent if, and only it generated by subalgebra an upper block triangular matrix algebra, A:=UTZ2⁎(A1,…,Am), equipped suitable elementary Z2-grading involution. Here we give necessary sufficient conditions so IdZ2⁎(A) factorizes in the product ideals polynomial identities its simple components Ai.