... a Gorenstein ring, then ST/ITis again a Gorensteinring for almost all α.Proof. We first will recall the definition about the Gorenstein ring. A Noetherian ring is a Gorensteinring if its ... respect to α. The definition of φαdoes not depend on the choice of the bases of F, G in the sense that if Bis the matrix of φ with respect to other bases of F, G, then there are bases of Fα, ... haveinj.dim(Lα) = i nj.dim (L). In p articula r, if L is an inj ective module, then Lαis also an injective module.Proof. Since S and Sαhave finite global dimensions, therefore inj.dimL and...