PI-RINGS WITH ARTINIAN PROPER CYCLICS ARE NOETHERIAN

Authors : Adel N ALAHMADİ

Pages : 40-42

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Publication Date : 2013-06-01

Article Type : Research Paper

Abstract :Non-Artinian algebras over which proper cyclic right modules are Artinian must be right Ore domains. It is shown that if R is a PI-ring whose proper cyclic right R-modules are Artinian, then R is right Noetherian. In particular, if G is a solvable group and each proper cyclic right K[G]-module is Artinian, then the group algebra K[G] is Noetherian. It is also shown that for a group algebra K[G], if every proper cyclic right K[G]-module is Artinian and K-finite dimensional, then K[G] is Noetherian.
Keywords : group algebra, proper cyclic, Artinian ring, Noetherian ring