Alejandro ALVARADO-GARCİA, César CEJUDO-CASTİLLA, Hugo Alberto RİNCONMEJİA, Ivan Fernando VİLCHİS -MONTALVO, Manuel Gerardo ZORRİLLA- NORİEGA

On QF rings and artinian principal ideal rings

Yayın Aralığı: 6
Başlangıç: 2002
Yayıncı: Hacettepe Üniversitesi Fen Fakultesi

In this work we give sufficient conditions for a ring $R$ to be quasi-Frobenius, such as $R$ being left artinian and the class of injective cogenerators of $R$-Mod being closed under projective covers. We prove that $R$ is a division ring if and only if $R$ is a domain and the class of left free $R$-modules is closed under injective hulls. We obtain some characterizations of artinian principal ideal rings. We characterize the rings for which left cyclic modules coincide with left cocyclic $R$-modules. Finally, we obtain characterizations of left artinian and left coartinian rings.

Keywords:

left artinian ring, artinian principal ideal ring conoetherian ring, coartinian ring, QF ring, perfect ring, semiartinian ring,

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