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Almost preenvelopes of commutative rings. (English) Zbl 1267.13018
Summary: We study almost \(F\)-preenvelopes in the category of rings, for a significative class \(F\) of commutative rings. We completely identify those rings which have an almost \(F\)-preenvelope when \(F\) is the class of fields, semisimple rings, integer domains and local rings. We show that rings with Krull dimension zero have (almost) \(V\)-preenvelopes, where \(V\) is the class of von Neumann regular rings.
MSC:
13C05 Structure, classification theorems for modules and ideals in commutative rings
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