A Note on Types of Noetherian Local Rings

Abstract

In this note we investigate some results which concern the typesof local rings. In particular it is shown that if the type of aquasi-unmixed local ring A is less than or equal tomathrm{depth} ,A + 1, and hat{A}_{p} is Cohen-Macaulay forevery prime p not= hat{m}, then A is Cohen-Macaulay. (Thisimplies the previously known result: if hat{A} satisfies(S_{n-1}), where n is the type of a ring A, then A isCohen-Macaulay.)