In this paper,we discuss the structure of intuitionistic fuzzy(IF)homomorphisms,exact sequences and some other concepts in category of IF modules.We study on IF exact sequences and IF Hom functors in IFR-Mod and obtai...In this paper,we discuss the structure of intuitionistic fuzzy(IF)homomorphisms,exact sequences and some other concepts in category of IF modules.We study on IF exact sequences and IF Hom functors in IFR-Mod and obtain some results about them.If R is a commutative ring and 0→A~f→B~g→C is an exact sequence in IFR-Mod,where f is IF split homomorphism,then we show that Hom_(IF-R)(D,-)preserves the sequence for every D∈IFR-Mod.Also IF projective modules will be introduced and investigated in this paper.Finally we define product and coproduct of IF modules and show that if M is an R-module,A=(μ_(A),ν_(A))≤_(IF)M and e_(i)∈E(R)for any i∈I,then Hom(Пi2I 0IF Rei;A)=Πi2I Hom(0IF Rei;A).展开更多
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
文摘In this paper,we discuss the structure of intuitionistic fuzzy(IF)homomorphisms,exact sequences and some other concepts in category of IF modules.We study on IF exact sequences and IF Hom functors in IFR-Mod and obtain some results about them.If R is a commutative ring and 0→A~f→B~g→C is an exact sequence in IFR-Mod,where f is IF split homomorphism,then we show that Hom_(IF-R)(D,-)preserves the sequence for every D∈IFR-Mod.Also IF projective modules will be introduced and investigated in this paper.Finally we define product and coproduct of IF modules and show that if M is an R-module,A=(μ_(A),ν_(A))≤_(IF)M and e_(i)∈E(R)for any i∈I,then Hom(Пi2I 0IF Rei;A)=Πi2I Hom(0IF Rei;A).
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.
