Proceedings of the Edinburgh Mathematical Society (Series 2)

Research Article

The co-localization of an Artinian module

Leif Melkerssona1 and Peter Schenzela2*

a1 University of Lund Department of Mathematics Box 118, S-221 00 Lund, Sweden

a2 Max-Planck-Gesellschaft AG Algebraische Geometrie und Zahlentheorie Jägerstr. 10-11 D-10 117 Berlin, Germany

Abstract

For a multiplicative set S of a commutative ring R we define the co-localization functor HomR(Rs,xs22C5). 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.

(Received June 01 1993)

Footnotes

* During the preparation of this note the second named author was supported by the United Kingdom SERC (Grant No. F 55584).