Block-triangular matrix algebras and factorable ideals of graded polynomial identities

We study the graded polynomial identities of block-triangular matrix algebras with respect to the grading defined by an abelian group G. In particular, we describe conditions for the TG-ideal of a such algebra to be factorable as a product of TG-ideals corresponding to the algebras defining the diagonal blocks. Moreover, for the factorable T2-ideal of a superalgebra we give a formula for computing its sequence of graded cocharacters once given the sequences of cocharacters of the T2-ideals that factorize it. We finally apply these results to a specific example of block-triangular matrix superalgebra.