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- 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's book. A semiperfect ring is a ring over which every finitely generated left module has a projective cover. This property is left-right symmetric. (en)
- 환론에서 반완전환(半完全環, 영어: semiperfect ring)은 모든 유한 생성 가군이 사영 덮개를 갖는 환이다. (ko)
- 環論という抽象代数学の分野において、左完全環 (left perfect ring) はすべての左加群が射影被覆をもつような環のことである。右完全環も同様に定義される。条件は左右対称でない、つまり、一方の側で完全だがもう一方では完全でないような環が存在する。完全環は で導入された。 半完全環 (semiperfect ring) はすべての有限生成左加群が射影被覆をもつような環である。この性質は左右対称的である。 (ja)
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- 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's book. A semiperfect ring is a ring over which every finitely generated left module has a projective cover. This property is left-right symmetric. (en)
- 환론에서 반완전환(半完全環, 영어: semiperfect ring)은 모든 유한 생성 가군이 사영 덮개를 갖는 환이다. (ko)
- 環論という抽象代数学の分野において、左完全環 (left perfect ring) はすべての左加群が射影被覆をもつような環のことである。右完全環も同様に定義される。条件は左右対称でない、つまり、一方の側で完全だがもう一方では完全でないような環が存在する。完全環は で導入された。 半完全環 (semiperfect ring) はすべての有限生成左加群が射影被覆をもつような環である。この性質は左右対称的である。 (ja)
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- 完全環 (ja)
- 반완전환 (ko)
- Perfect ring (en)
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