Perfect ring

In the area of abstract algebra known as ring theory, a left perfect ring is a type of ring in 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 1960). In the area of abstract algebra known as ring theory, a left perfect ring is a type of ring in 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 1960). A semiperfect ring is a ring over which every finitely generated left module has a projective cover. This property is left-right symmetric. The following equivalent definitions of a left perfect ring R are found in (Anderson,Fuller & 1992, p.315): For a left perfect ring R: Let R be ring. Then R is semiperfect if any of the following equivalent conditions hold: