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

 

The fundamental module of a normal local domain of dimension $ 2$


Authors: Yuji Yoshino and Takuji Kawamoto
Journal: Trans. Amer. Math. Soc. 309 (1988), 425-431
MSC: Primary 13H10; Secondary 13C13, 14B05, 14J17
MathSciNet review: 957079
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Abstract: The fundamental module $ E$ of a normal local domain $ (R,\,\mathfrak{m})$ of dimension $ 2$ is defined by the nonsplit exact sequence $ 0 \to K \to E \to \mathfrak{m} \to 0$, where $ K$ is the canonical module of $ R$. We prove that, if $ R$ is complete with $ R/\mathfrak{m} \simeq \mathbb{C}$, then $ E$ is decomposable if and only if $ R$ is a cyclic quotient singularity. Various other properties of fundamental modules will be discussed.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1988-0957079-7
PII: S 0002-9947(1988)0957079-7
Keywords: Local rings, reflexive modules, quotient singularities, Cohen-Macaulay modules, canonical modules, Auslander-Reiten quivers
Article copyright: © Copyright 1988 American Mathematical Society