Research Letter

A test criterion for categorically compact rings

Editorial Office
Suid-Afrikaanse Tydskrif vir Natuurwetenskap en Tegnologie | Vol 12, No 4 | a570 | DOI: | © 1993 Editorial Office | This work is licensed under CC Attribution 4.0
Submitted: 09 July 1993 | Published: 09 July 1993

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Editorial Office,, South Africa

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The Kuratowski-Mrowka theorem - a topological space X is compact if and only if for each space Y the second projection map ∏₂:X x Y → Y is a closed map - provides for a categorical interpretation of compactness once a suitable notion of closure is obtained. In this article we study a general notion of compactness with respect to a class F of ring’s that is either hereditary semisimple or quotient reflective. We show that to test for categorical compactness of a ring R we need only check R R F, where R F = ∩{D D is an ideal of R and RD є F} , and to test ∏₂:(RRF)x H → H for rings H belonging to F as opposed to arbitrary H.


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