Let R be a ring with identity, and R-ill denote the set of all left topologizing filters on R. In this paper, we give a sufficient condition for the commutativity of R-ill under the hypothesis of left Noetherianness, ...Let R be a ring with identity, and R-ill denote the set of all left topologizing filters on R. In this paper, we give a sufficient condition for the commutativity of R-ill under the hypothesis of left Noetherianness, as well as some examples.展开更多
Let R ＊θ G be the skew group ring with a F.C group G and the group homomrphism 8 from G to Aut（R）, the group of automorphisms of the ring R. In this paper,the necessary and sufficient condition such that R ＊θ G ...Let R ＊θ G be the skew group ring with a F.C group G and the group homomrphism 8 from G to Aut（R）, the group of automorphisms of the ring R. In this paper,the necessary and sufficient condition such that R ＊θ G will be Noetherian is given, which generalizes the results of LG. connel.展开更多
A ring R is said to be right U-Noetherian if R satisfies ascending chain condition （ACC） on uniform right ideals. This article characterizes U-Noetherian ring by U-injective modules and discusses the extensions of U...A ring R is said to be right U-Noetherian if R satisfies ascending chain condition （ACC） on uniform right ideals. This article characterizes U-Noetherian ring by U-injective modules and discusses the extensions of U-Noetherian ring.展开更多
Let R be a Noetherian ring. The projectivity and injectivity of modules over R are discussed. The concept of modules is introduced and the descriptions for co-*-modules over R are given. At last, cotilting modules ove...Let R be a Noetherian ring. The projectivity and injectivity of modules over R are discussed. The concept of modules is introduced and the descriptions for co-*-modules over R are given. At last, cotilting modules over R are characterized by means of co-*-modules.展开更多
文摘Let R be a ring with identity, and R-ill denote the set of all left topologizing filters on R. In this paper, we give a sufficient condition for the commutativity of R-ill under the hypothesis of left Noetherianness, as well as some examples.
基金Supported by the NSF of Educational Department of Henan Province(20025100003)
文摘Let R ＊θ G be the skew group ring with a F.C group G and the group homomrphism 8 from G to Aut（R）, the group of automorphisms of the ring R. In this paper,the necessary and sufficient condition such that R ＊θ G will be Noetherian is given, which generalizes the results of LG. connel.
基金Supported by the Scientific Research Foundation of Gansu Provincial Education Department (0813B-01)
文摘A ring R is said to be right U-Noetherian if R satisfies ascending chain condition （ACC） on uniform right ideals. This article characterizes U-Noetherian ring by U-injective modules and discusses the extensions of U-Noetherian ring.
文摘Let R be a Noetherian ring. The projectivity and injectivity of modules over R are discussed. The concept of modules is introduced and the descriptions for co-*-modules over R are given. At last, cotilting modules over R are characterized by means of co-*-modules.
