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 Fbe a locally defined formation consisting of locally soluble groups, G a hyper-(cyclic or finite) locally soluble group and A a noetherian ZG-module with all irreducible ZG-factors being finite, G∈F, f(∞)f(p), ...Let Fbe a locally defined formation consisting of locally soluble groups, G a hyper-(cyclic or finite) locally soluble group and A a noetherian ZG-module with all irreducible ZG-factors being finite, G∈F, f(∞)f(p), f(p)≠ for each p∈π. The following conclutions are obtained: (1) if there exists a maximal submodule B of A such that A/B is F-central in G and B has no nonzero F-central ZG-factors, then A has an F-decomposition; (2) if there exists an irreducible F-central submodule B of A such that all ZG-composition factors of A/B are F-ecentric, then A has an F-decomposition.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
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TheNationalNaturalScienceFoundationofChina (No .10 1710 74 )
文摘Let Fbe a locally defined formation consisting of locally soluble groups, G a hyper-(cyclic or finite) locally soluble group and A a noetherian ZG-module with all irreducible ZG-factors being finite, G∈F, f(∞)f(p), f(p)≠ for each p∈π. The following conclutions are obtained: (1) if there exists a maximal submodule B of A such that A/B is F-central in G and B has no nonzero F-central ZG-factors, then A has an F-decomposition; (2) if there exists an irreducible F-central submodule B of A such that all ZG-composition factors of A/B are F-ecentric, then A has an F-decomposition.
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.
