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The co-localization of an Artinian module

  • Leif Melkersson (a1) and Peter Schenzel (a2)
Abstract

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.

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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

8. D. G. Northcott , Generalized Koszul complexes and Artinian modules, Quart. J. Math. Oxford (2) 23 (1972), 289297.

11. R. Y. Sharp , A method for the study of Artinian modules, with an application to asymptotic behavior, in: Commutative Algebra (Math. Sciences Research Inst. Publ., No. 15, Springer-Verlag, 1989), 443465.

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Proceedings of the Edinburgh Mathematical Society
  • ISSN: 0013-0915
  • EISSN: 1464-3839
  • URL: /core/journals/proceedings-of-the-edinburgh-mathematical-society
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