Finitistic dimension and endomorphism algebras of W-Gorenstein modules

摘要

Let A be an artin algebra, M be a W-Gorenstein A-module and B = End(A)M, then M is a A-B-bimodule. We use the restricted flat dimension of M-B and the finitistic W-dimension of A to characterize the finitistic dimension of B, and obtain the following main result: if A is G(W)-finite with G(W)(A) = add(A)E, then we have: (1) If findim(W)A = 0 or 1, then findimB <= 2 + rfd(M-B) + pd(B)Hom(A)(M, E); (2) If findim(W)A >= 2, then findimB <= findim(W)(A) + rfd(M-B) + pd(B)Hom(A)(M, E).