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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.
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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