On Covers and Envelopes in Some Functor Categories.

We study the existence of covers and envelopes by some special functors on the category of finitely presented modules. As an application, we characterize some important rings using these functors. We also investigate homological properties of some functors on the stable module category. The relationship between phantoms and Ext-phantoms is obtained. It is shown that every leftR-moduleMhas an Ext-phantom preenvelopef:M → Nwith coker(f) pure-projective. Finally, we prove that, as a torsionfree class of (mod-R, Ab), (mod-R, Ab) is generated by theFP-injective objects. [ABSTRACT FROM AUTHOR]