Several Kinds Of (∈,∈ ∨q_ (λ,μ) )-Fuzzy Ideals Of Semigroups And The Characterization Of Drazin Semigroups

In this paper, we give the definitions of (∈,∈∨q_(λ,μ))- fuzzy Drazin subsemigroups, (∈,∈∨q_(λ,μ))- fuzzy n-pseudo ideals, (∈,∈∨q_(λ,μ))- fuzzy completely prime ideals, (∈,∈∨q_(λ,μ))- fuzzy k-ideals, generalized fuzzy n-pseudo ideals, generalized fuzzy completely prime ideals and generalized fuzzy k-ideals, we study the Drazin semigroup by using the generalized fuzzy subsystem of semigroups, and characterize semisimple semigroups by using generalized fuzzy ideals and the properties of fuzzy ideals generated by fuzzy points, and we obtain some properties.In Chapter two, we introduce the definitions of an (∈,∈∨q_(λ,μ))- fuzzy subgroupoid and an (∈,∈∨q_(λ,μ))- fuzzy Drazin subsemigroup, and discuss the equivalence conditions between (∈,∈∨q_(λ,μ))- fuzzy Drazin subsemigroups and (∈,∈∨q_(λ,μ))- fuzzy subgroupoids.In Chapter three, we give the concepts of fuzzy n-pseudo ideals(bi-ideals, interior ideals) of semigroups, and study the equivalence conditions of (∈,∈∨q_(λ,μ))- fuzzy n-pseudo ideals (bi-ideals, interior ideals) and generalized fuzzy n-pseudo ideals (bi-ideals, interior ideals).In Chapter four, we introduce the definition of (∈,∈∨q_(λ,μ))- fuzzy completely prime ideals, get the relationship between (∈,∈∨q_(λ,μ))- fuzzy completely prime ideals and level subsets; Besides, we discuss the ascending (descending) chain conditions about completely prime ideals and some of fundamental properties of them.In Chapter five, we introduce the definition of k-ideals into semigroups and give the concepts of generalized fuzzy k-ideals, (∈,∈∨q_(λ,μ))- fuzzy k-ideals, and discuss the equivalence relationship between them. Besides, we give the concept of generalized fuzzy characteristic and obtain some elementary results, including charactering it by using level ideals. We also state the product of generalized fuzzy k-ideals in semigroups.In Chapter six, we study the Drazin semigroup by using the generalized fuzzy subsystem of semigroup. We get better results.In Chapter seven, we characterize semisimple semigroups by using generalized fuzzy ideals and the properties of fuzzy ideals generated by fuzzy points, and we obtain some properties.