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:

单词	PerfectAndSemiperfectRings
释义	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 $k$ .
随便看	ZeroElements zero elements ZeroesOfAnalyticFunctionsAreIsolated zeroes of analytic functions are isolated ZeroIdeal zero ideal zero ideal ZeroIdeal1 ZeroMap zero map ZeroMatrix zero matrix ZeroModule zero module ZeroOfAFunction zero of a function ZeroOfPolynomial zero of polynomial ZeroPolynomial zero polynomial ZeroRing zero ring ZeroRuleOfProduct zero rule of product ZerosAndPolesOfRationalFunction