# Semiperfect ring

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In abstract algebra, a semiperfect ring is a ring over which every finitely generated left module has a projective cover. This property is left-right symmetric.

## Definition

Let R be ring. Then R is semiperfect if any of the following equivalent conditions hold:

## Examples

Examples of semiperfect rings include:

## Properties

Since a ring R is semiperfect iff every simple left R-module has a projective cover, every ring Morita equivalent to a semiperfect ring is also semiperfect.

## References

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