On Takahashi's questions about dominant local rings

Abstract

This article studies dominant local rings, a notion introduced by Takahashi. We prove that, for a flat local homomorphism R-->S between commutative noetherian local rings, dominance descends from S to R, thereby answering a question of Takahashi affirmatively. We also establish several sufficient conditions under which a Cohen-Macaulay local ring of finite CM type is dominant, supporting a conjecture of Takahashi.