SOME REMARKS ON TYPES OF NOETHERIAN LOCAL RINGS

Abstract

We study some results which concern the types of Noetherian local rings, and improve slightly the previous result: For a complete unmixed (or quasi-unmixed) Noetherian local ring A, we prove that if either Ap is Cohen-Macaulay, or r(Ap) ≤ depth Ap + 1 for every prime ideal p in A, then A is Cohen-Macaulay. Also, some analogous results for modules are considered.

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