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Categorical compactness for rings

Published online by Cambridge University Press:  09 April 2009

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.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1995

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