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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