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 finitely-generated $R$-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 left-right symmetric property.

Some examples of semiperfect rings include:

1. perfect rings;

2. left/right Artinian rings;

3. finite-dimensional algebras over a field $k$.

Title	perfect and semiperfect rings
Canonical name	PerfectAndSemiperfectRings
Date of creation	2013-03-22 19:17:56
Last modified on	2013-03-22 19:17:56
Owner	joking (16130)
Last modified by	joking (16130)
Numerical id	4
Author	joking (16130)
Entry type	Definition
Classification	msc 16D40