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
By employing function one-direction S-rough sets and rough law generation method based on function S-rough sets, ^-f-decomposition law and ^-F-decomposition rough law are proposed, and the measurement of rough law var...By employing function one-direction S-rough sets and rough law generation method based on function S-rough sets, ^-f-decomposition law and ^-F-decomposition rough law are proposed, and the measurement of rough law variation in the process of rough law ^-F-decomposition is researched. The concepts of law energy and attdbute ^-f-interference degree are presented, which make the variation of rough law become measurable. ^-f-decomposition law energy characteristic theorem, ^-f- decomposition law energy inequality theorem, ^-F-decomposition rough law energy characteristic theorem, and ^-f-decomposition law energy mean value theorem are presented.展开更多
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 Natural Science Foundation of Shandong Province (Y2007H02)
文摘By employing function one-direction S-rough sets and rough law generation method based on function S-rough sets, ^-f-decomposition law and ^-F-decomposition rough law are proposed, and the measurement of rough law variation in the process of rough law ^-F-decomposition is researched. The concepts of law energy and attdbute ^-f-interference degree are presented, which make the variation of rough law become measurable. ^-f-decomposition law energy characteristic theorem, ^-f- decomposition law energy inequality theorem, ^-F-decomposition rough law energy characteristic theorem, and ^-f-decomposition law energy mean value theorem are presented.
