Abstract
Giambruno and Zaicev stated that, over a field of characteristic zero, T-ideals of minimal varieties of a fixed exponent have the factoring property. In the present article, we describe necessary and sufficient conditions for the factorability of T2-ideals of minimal supervarieties of a fixed superexponent. In light of the characterization of minimal supervarieties of a fixed superexponent given by Di Vincenzo, da Silva, and Spinelli, the crucial point is the study of the factorability of T2-ideals of the upper-block triangular matrix algebras equipped with an elementary -grading, where are simple superalgebras. We obtain necessary and sufficient conditions for the isomorphism between two superalgebras . We also show that the concept of -regularity establishes a nice connection between the factorability of the T2-ideal of and the number of isomorphism classes of .
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