perfect and semiperfect rings
A ring $R$ is called left/right perfect if for any left/right $R$module $M$ there exists a projective cover $p:P\to M$.
A ring $R$ is called left/right semiperfect if for any left/right finitelygenerated $R$module $M$ there exists a projective cover $p:P\to M$.
It can be shown that there are rings which are left perfect, but not right perfect. However being semiperfect is leftright symmetric^{} property.
Some examples of semiperfect rings include:

1.
perfect rings;

2.
left/right Artinian rings;

3.
finitedimensional^{} algebras over a field $k$.
Title  perfect and semiperfect rings 

Canonical name  PerfectAndSemiperfectRings 
Date of creation  20130322 19:17:56 
Last modified on  20130322 19:17:56 
Owner  joking (16130) 
Last modified by  joking (16130) 
Numerical id  4 
Author  joking (16130) 
Entry type  Definition 
Classification  msc 16D40 