Perfect ring

In the area of abstract algebra known as ring theory, a left perfect ring is a type of ring over which all left modules have projective covers. The right case is defined by analogy, and the condition is not left-right symmetric; that is, there exist rings which are perfect on one side but not the other. Perfect rings were introduced in Bass's book.

This article is about perfect rings as introduced by Hyman Bass. For perfect rings of characteristic p generalizing perfect fields, see perfect field.

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

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