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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A test theorem on coherent GCD domains


Author: Yi Cai Zhao
Journal: Proc. Amer. Math. Soc. 115 (1992), 47-49
MSC: Primary 13G05; Secondary 13F15
MathSciNet review: 1092932
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Abstract: Let $ R$ be a commutative indecomposable coherent ring. Then the following statements are equivalent: (i) $ R$ is a GCD domain; (ii) $ {R_M}$ is a GCD domain for every maximal ideal of $ M$ of $ R$, and every finitely generated projective ideal in $ R$ is principal; (iii) every two-generated ideal in $ R$ has finite projective dimension, and every finitely generated projective ideal in $ R$ is principal. Auslander-Buchsbaum's Theorem, etc. can be obtained from the result above.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1992-1092932-4
PII: S 0002-9939(1992)1092932-4
Article copyright: © Copyright 1992 American Mathematical Society