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Categorical compactness for rings

Part of: General theory of categories and functors

Published online by Cambridge University Press:  09 April 2009

Temple H. Fay  and
Stephan V. Joubert
Temple H. Fay
Affiliation:
The University of Southern MississippiHattiesburg, MS, USA
Stephan V. Joubert
Affiliation:
The Technikon Pretoria Pretoria West 0001, South Africa
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Abstract

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In this paper we study categorical compactness with respect to a class of objects F being motiveated by examples arising from modules, abelian groups, and various classes of non-abelian groups. This theory is then applied to the category of not necessarily associative rings. In particular, we study the example arising from the class of all torsion-free rings. This work extends some recent results of B. J. Gardner for associative rings and radical classes.

Keywords

torsion theorysemisimplepolynomial regularityclosure operatorcategorical compactness.

MSC classification

Secondary: 18A20: Epimorphisms, monomorphisms, special classes of morphisms, null morphisms
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 59 , Issue 3 , December 1995 , pp. 313 - 329
Copyright
Copyright © Australian Mathematical Society 1995

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