Starke Kotorsionsmoduln
Identifieur interne : 000F28 ( Main/Exploration ); précédent : 000F27; suivant : 000F29Starke Kotorsionsmoduln
Auteurs : H. Zöschinger [Allemagne]Source :
- Archiv der Mathematik [ 0003-889X ] ; 2003-08-01.
Abstract
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.
Url:
DOI: 10.1007/s00013-003-0818-9
Affiliations:
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