Three local conditions on a graded ring

Matijevic, Jacob

doi:10.1090/S0002-9947-1975-0384776-8

Three local conditions on a graded ring
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by Jacob Matijevic PDF

Trans. Amer. Math. Soc. 205 (1975), 275-284 Request permission

Abstract:

Let $R = {\Sigma _{i \in Z}}{R_i}$ be a commutative graded Noetherian ring with unit and let $A = {\Sigma _{i \in Z}}{A_i}$ be a finitely generated graded $R$ module. We show that if we assume that ${A_M}$ is a Cohen Macaulay ${R_M}$ module for each maximal graded ideal $M$ of $R$, then ${A_P}$ is a Cohen Macaulay ${R_P}$ module for each prime ideal $P$ of $R$. With $A = R$ we show that the same is true with Cohen Macaulay replaced by regular and Gorenstein, respectively.

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