In this article, we introduce the notion of fuzzy G-module by defining the group action of G on a fuzzy set of a Z-module M. We establish the cases in which fuzzy submodules also become fuzzy G-submodules. Notions of ...In this article, we introduce the notion of fuzzy G-module by defining the group action of G on a fuzzy set of a Z-module M. We establish the cases in which fuzzy submodules also become fuzzy G-submodules. Notions of a fuzzy prime submodule, fuzzy prime G-submodule, fuzzy semi prime submodule, fuzzy G-semi prime submodule, G-invariant fuzzy submodule and G-invariant fuzzy prime submodule of M are introduced and their properties are described. The homomorphic image and pre-image of fuzzy G-submodules, G-invariant fuzzy submodules and G-invariant fuzzy prime submodules of M are also established.展开更多
Proposition 1（Clifford Theorem）. Let G be finite. Consider a simple left A-module V. Then V is a finitely generated semisimple left A<sub>1</sub>-module. Let W be a simple left A<sub>1</sub>-...Proposition 1（Clifford Theorem）. Let G be finite. Consider a simple left A-module V. Then V is a finitely generated semisimple left A<sub>1</sub>-module. Let W be a simple left A<sub>1</sub>-submodule of V, and then I={g∈G|A<sub>1</sub>（?）<sub>A<sub>1</sub></sub> W（?）Ag（?）<sub>A<sub>1</sub></sub> W as A<sub>1</sub>-modules}is a subgroup of G, and there exists a natural number e such展开更多
In this paper we first improve the concentration- compactness lemma by proving that the vanishing case is a special case of dichotomy, then we apply this improved concentration- compactness lemma to a typical restrct...In this paper we first improve the concentration- compactness lemma by proving that the vanishing case is a special case of dichotomy, then we apply this improved concentration- compactness lemma to a typical restrcted minimization problem, and get some new results.展开更多
文摘In this article, we introduce the notion of fuzzy G-module by defining the group action of G on a fuzzy set of a Z-module M. We establish the cases in which fuzzy submodules also become fuzzy G-submodules. Notions of a fuzzy prime submodule, fuzzy prime G-submodule, fuzzy semi prime submodule, fuzzy G-semi prime submodule, G-invariant fuzzy submodule and G-invariant fuzzy prime submodule of M are introduced and their properties are described. The homomorphic image and pre-image of fuzzy G-submodules, G-invariant fuzzy submodules and G-invariant fuzzy prime submodules of M are also established.
文摘Proposition 1（Clifford Theorem）. Let G be finite. Consider a simple left A-module V. Then V is a finitely generated semisimple left A<sub>1</sub>-module. Let W be a simple left A<sub>1</sub>-submodule of V, and then I={g∈G|A<sub>1</sub>（?）<sub>A<sub>1</sub></sub> W（?）Ag（?）<sub>A<sub>1</sub></sub> W as A<sub>1</sub>-modules}is a subgroup of G, and there exists a natural number e such
基金Supported by the National Natural Science Foundation of China (No.19871030, 19771039) and Natural Science Foundation of Guangd
文摘In this paper we first improve the concentration- compactness lemma by proving that the vanishing case is a special case of dichotomy, then we apply this improved concentration- compactness lemma to a typical restrcted minimization problem, and get some new results.
