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Local rings of relatively small type are Cohen-Macaulay


Author: Takesi Kawasaki
Journal: Proc. Amer. Math. Soc. 122 (1994), 703-709
MSC: Primary 13H10; Secondary 13C14, 13D45
DOI: https://doi.org/10.1090/S0002-9939-1994-1215029-0
MathSciNet review: 1215029
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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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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1994-1215029-0
Keywords: Cohen-Macaulay ring, Cohen-Macaulay module, type of local ring
Article copyright: © Copyright 1994 American Mathematical Society

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