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On the Goldie dimension of injective modules*

Published online by Cambridge University Press:  20 January 2009

José L. Gómez Pardo  and
Pedro A. Guil Asensio
José L. Gómez Pardo
Affiliation:
Departamento de Alxebra, Universidade de Santiago, 15771 Santiago de Compostela, Spain E-mail address: pardo@zmat.usc.es
Pedro A. Guil Asensio
Affiliation:
Departamento de Matematicas, Universidad de Murcia, 30100 Espinardo, Murcia, Spain E-mail address: paguil@fcu.um.es
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Abstract

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Let M be an essentially finitely generated injective (or, more generally, quasi-continuous) module. It is shown that if M satisfies a mild uniqueness condition on essential closures of certain submodules, then the existence of an infinite independent set of submodules of M implies the existence of a larger independent set on some quotient of M modulo a directed union of direct summands. This provides new characterisations of injective (or quasi-continuous) modules of finite Goldie dimension. These results are then applied to the study of indecomposable decompositions of quasi-continuous modules and nonsingular CS modules.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 41 , Issue 2 , June 1998 , pp. 265 - 275
Copyright
Copyright © Edinburgh Mathematical Society 1998

References

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