Degenerations of covering functors

An algebra A admits a strong covering degeneration to the algebra A(R/G), provided “it can be covered by the category R via an almost Galois G-covering of integral type” (Theorem 2.6 and Corollary 2.6). We also prove that for a degeneration of the covering functors F1:R→A1 to F0:R→A0, the endomorphism algebra is a degeneration of the algebra , for any φ-invariant module N in mod R, provided they have the same k-dimension (see Theorem 3.1). Finally, for an almost Galois G-covering F1 of integral type, for all g∈G, under some conditions on N in mod R (Theorem 3.4 and Corollary 3.4). In consequence, the stability of the module variety dimensions under a strong covering degeneration process holds for some special dimension vectors (Theorem 3.5).