On module variety dimension for coverings and degenerations of algebras

Given a pair of G-covering functors F1:R→R1 and F0:R→R0 such that F0 is a Galois covering, the inequality for all z,t, of the dimensions of the first kind module sets under some assumptions is proved (Theorem 2.2). The result is applied to show the equality of the module variety dimensions for some special degenerations of algebras. Certain consequences for preserving wild and tame representation types by G-covering functors are also presented (Theorems 2.4 and 3.1).