an:06093363
Zbl 1252.13005
Parra, C.; Parra, R.; Rada, J.
Almost preenvelopes of commutative rings
EN
Int. J. Algebra 6, No. 9-12, 595-603 (2012).
00307799
2012
j
13C05 16S10 18B99
almost preenvelopes; semiprimitive rings; local rings; von Neumann regular rings
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.