Research Letter

A test criterion for categorically compact rings

Editorial Office
Suid-Afrikaanse Tydskrif vir Natuurwetenskap en Tegnologie | Vol 12, No 4 | a570 | DOI: https://doi.org/10.4102/satnt.v12i4.570 | © 1993 Editorial Office | This work is licensed under CC Attribution 4.0
Submitted: 09 July 1993 | Published: 09 July 1993

About the author(s)

Editorial Office,, South Africa

Full Text:

PDF (120KB)

Share this article

Bookmark and Share

Abstract

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.

Keywords

No related keywords in the metadata.

Metrics

Total abstract views: 850
Total article views: 773

Reader Comments

Before posting a comment, read our privacy policy.

Post a comment (login required)

Crossref Citations

No related citations found.