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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.[1]
A semiperfect ring is a ring over which every finitely generated left module has a projective cover. This property is left-right symmetric.