Some properties of uniform fuzzy modules and semiuniform fuzzy modules

In this thesis, we study some properties of uniform fuzzy modules and semiuniform fuzzy modules. Let R be a ring with the identity and M a right R-module. A submodule A of a right R-module M is called an essential submodule of M, if any non-zero submodule B of M, A∩B≠{θ} where θ is the zero element in M. A right R-module M is called a uniform module, if any non-zero submodule of M is an essential submodule of M. A submodule α of a fuzzy module μ in a right R-module M is called an essential submodule of μ, if any non-zero submodule β of μ, α∩β≠χ_θ. A fuzzy module μ in a right R-module M is called a uniform fuzzy module in M, if any non-zero submodule of μ is an essential submodule of μ. We would like to study relationship between uniform modules and uniform fuzzy modules. After that we introduce the concept of semiuniform fuzzy modules. A submodule A of a right R-module M is called a semiessential submodule of M, if any non-zero prime submodule P of M, A∩P≠{θ}. A right R-module M is called a semiuniform module, if any non-zero submodule of M is a semiessential submodule of M. A submodule α of a fuzzy module μ in a right R-module M is called a semiessential submodule of μ, if any non-zero prime submodule ρ of μ, α∩ρ≠χ_θ. A fuzzy module μ in a right R-module M is called a semiuniform fuzzy module in M, if any non-zero submodule of μ is a semiessential submodule of μ. We would like to study relationship between uniform fuzzy modules and semiuniform fuzzy modules.