This doctoral thesis provides several new results in which we leverage the inner structure of non-singular rings, in particular of self-injective von Neumann regular rings. First, we describe categorical and set-theoretical conditions under which all products of compact objects remain compact, where the notion of compactness is relativized with respect to a fixed subclass of objects. A special instance when such closure property holds are the classic module categories over rings of our interest. Moreover, we show that a potential counterexample for Köthe's Conjecture might be in the form of a countable local subring of a suitable simple self-injective von Neumann regular ring. 1
| Identifer | oai:union.ndltd.org:nusl.cz/oai:invenio.nusl.cz:434348 |
| Date | January 2020 |
| Creators | Kálnai, Peter |
| Contributors | Žemlička, Jan, Breaz, Simion, Příhoda, Pavel |
| Source Sets | Czech ETDs |
| Language | English |
| Detected Language | English |
| Type | info:eu-repo/semantics/doctoralThesis |
| Rights | info:eu-repo/semantics/restrictedAccess |
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