Invariant properties of representations under excellent extensions

In this paper, we introduce the notion of weak excellent extensions of rings as a generalization of that of excellent extensions of rings. Let Γ be a weak excellent extension of an Artinian algebra Λ. We prove that if Λ is of finite representation type (resp. CM-finite, CM-free), then so is Γ; furthermore, if Γ is an excellent extension of Λ, then the converse also holds true. We also study when the representation dimension of an Artinian algebra is invariant under excellent extensions.