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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Three local conditions on a graded ring


Author: Jacob Matijevic
Journal: Trans. Amer. Math. Soc. 205 (1975), 275-284
MSC: Primary 13C15; Secondary 13H10
MathSciNet review: 0384776
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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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1975-0384776-8
PII: S 0002-9947(1975)0384776-8
Keywords: Graded ring, graded ideal, Cohen-Macaulay, local ring, Gorenstein local ring, rank, Krull dimension, grade
Article copyright: © Copyright 1975 American Mathematical Society