Almost preenvelopes of commutative rings. (English) Zbl 1252.13005

Parra, C.; Parra, R.; Rada, J.

Int. J. Algebra 6, No. 9-12, 595-603 (2012).

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

Keywords:

almost preenvelopes; semiprimitive rings; local rings; von Neumann regular rings