’n Toetskriterium vir kategorieel kompakte ringe
Suid-Afrikaanse Tydskrif vir Natuurwetenskap en Tegnologie/South African Journal of Science and Technology
| Field | Value | |
| Title | ’n Toetskriterium vir kategorieel kompakte ringe A test criterion for categorically compact rings | |
| Creator | Office, Editorial | |
| Description | Eienskappe en verbande tussen die topologiese begrippe "kompak" en “Hausdorff' kan meer abstrak bestudeer word, met behoud van eienskappe en verbande. Die Kuratowski-Mrówka stelling maak dit moontlik om kompaktheid in kategorieë te bestudeer nadat 'n geskikte geslotenheidsbegrip uitgevoer is. Dit word via kategoriële afsluitoperatore bereik. 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. | |
| Publisher | AOSIS | |
| Date | 1993-07-09 | |
| Identifier | 10.4102/satnt.v12i4.570 | |
| Source | Suid-Afrikaanse Tydskrif vir Natuurwetenskap en Tegnologie; Vol 12, No 4 (1993); 89-90 Suid-Afrikaanse Tydskrif vir Natuurwetenskap en Tegnologie; Vol 12, No 4 (1993); 89-90 2222-4173 0254-3486 | |
| Language | eng | |
| Relation |
The following web links (URLs) may trigger a file download or direct you to an alternative webpage to gain access to a publication file format of the published article:
https://journals.satnt.aosis.co.za/index.php/satnt/article/view/570/1020
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