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Almost preenvelopes of commutative rings. (English) Zbl 1252.13005
Summary: We study almost \(\mathcal F\)-preenvelopes in the category of rings, for a significative class \(\mathcal F\) of commutative rings. We completely identify those rings which have an almost \(\mathcal F\)-preenvelope when \(\mathcal F\) is the class of fields, semisimple rings, integer domains and local rings. We show that rings with Krull dimension zero have (almost) \(\mathcal V\)-preenvelopes, where \(\mathcal V\) is the class of von Neumann regular rings.
MSC:
13C05 Structure, classification theorems for modules and ideals in commutative rings
16S10 Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.)
18B99 Special categories
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