Local rings of relatively small type are Cohen-Macaulay

Kawasaki, Takesi

doi:10.1090/S0002-9939-1994-1215029-0

Local rings of relatively small type are Cohen-Macaulay
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Proc. Amer. Math. Soc. 122 (1994), 703-709 Request permission

Abstract:

Let A be a local ring of type n. It is known that if $n = 1$, then A is Cohen-Macaulay and that if $n = 2$ and A is unmixed, then A is Cohen-Macaulay. Then let $n \geq 3$. What makes A Cohen-Macaulay? We show that if A contains a field and $\hat A$ satisfies $({S_{n - 1}})$, then A is Cohen-Macaulay.

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