Starke Kotorsionsmoduln |
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Authors: | H Zöschinger |
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Institution: | (1) Mathematisches Institut, Universität München, Theresienstr. 39, 80333 München, Germany |
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Abstract: | Suppose that $(R, m)$ is a noetherian local ring and that E is the
injective hull of the residue class field $R/m$. Suppose that M is an
R-module, $M^0 = {\mbox{\rm Hom}}_R (M, E)$ is the Matlis dual of
M and ${\mbox{\rm Coass}(M)} = {\mbox{\rm Ass} (M^0)}$. M is
called cotorsion if every prime ideal ${\frak p} \in {\mbox{\rm Coass}}(M)$ is
regular; it is called strongly cotorsion if $\cap {\rm Coass}(M)$ is regular.
In the first part, we completely describe the structure of the strongly
cotorsion modules over R, use this to determine the coassociated prime
ideals of the bidual $M^{00}$, and give in the second part
criteria for a cotorsion module being strongly cotorsion.
Received: 7 March 2002 |
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Keywords: | 13B35 13C12 13D45 |
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