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The co-localization of an Artinian module

Published online by Cambridge University Press:  20 January 2009

Leif Melkersson  and
Peter Schenzel
Leif Melkersson
Affiliation:
University of LundDepartment of MathematicsBox 118, S-221 00 Lund, Sweden
Peter Schenzel
Affiliation:
Max-Planck-GesellschaftAG Algebraische Geometrie und ZahlentheorieJägerstr. 10-11D-10 117 Berlin, Germany
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Abstract

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For a multiplicative set S of a commutative ring R we define the co-localization functor HomR(Rs,⋅). It is a functor on the category of R-modules to the category of Rs-modules. It is shown to be exact on the category of Artinian R-modules. While the co-localization of an Artinian module is almost never an Artinian Rs-module it inherits many good properties of A, e.g. it has a secondary representation. The construction is applied to the dual of a result of Bourbaki, a description of asymptotic prime divisors and the co-support of an Artinian module.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 38 , Issue 1 , February 1995 , pp. 121 - 131
Copyright
Copyright © Edinburgh Mathematical Society 1995

References

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