Our aim in this paper is to introduce and study a new sort of fuzzy ternary subsemigroup (left ideal, right ideal, lateral ideal, quasi-ideal, bi-ideal) of a ternary semigroup, called interval-valued (α,β )-fuzzy ternary subsemigroup (left ideal, right ideal, lateral ideal, quasi-ideal, bi-ideal). We also characterize regular ternary semigroups in terms of these interval-valued fuzzy ideals.

In this paper, we introduce the concept of (α, β)-fuzzy ideals in ternary semigroups, which is a generalization of fuzzy ideals in ternary semigroups. We investigate the related properties of ternary semigroups. The lower and upper parts of fuzzy subsets of a ternary semigroup are defined. Characterizations of regular ternary semigroups by the properties of the lower part of (∈,∈∨q)-fuzzy left ...

The concept of q , -fuzzy ternary subsemigroup (left, right, lateral, quasi-, bi-) ideal of a ternary semigroup is introduced and several related properties are investigated. We give some characterizations of regular and weakly regular ternary semigroups by q , -fuzzy left (right, lateral) ideals, q , -fuzzy quasi-ideals and q , -fuzzy bi-(generalized bi-) ideals.

In this paper we introduce the notions of pure ideals, weakly pure ideals in ternary semigroups. We also de ne purely prime ideals of a ternary semigroup and study some properties of these ideals. The space of purely prime two-sided ideal is topologized.

In this note, we show that an ordered ternary semigroup is left and right simple if and only if it does not contain proper bi-ideals. The similar result is valid on ordered semigroups [7], on ordered Γ-semigroups [3] and on ternary semigroups [4]. Mathematics Subject Classification: 06F05

We provide a complete classification of the n-ary semigroup structures defined by polynomial functions over infinite commutative integral domains with identity, thus generalizing G lazek and Gleichgewicht’s classification of ternary semigroups.

In this paper we introduce the notion of fuzzy interior ideals in ternary semigroups and investigated relations between fuzzy ideals and fuzzy interior ideals in terms of regularity. Here a characterization of fuzzy interior ideals is obtained in terms of fuzzy translation operator. The notions of rough and rough fuzzy interior ideals in a ternary semigroup are introduced. Relation between cong...

In this paper, the concepts of irreducible and strongly pseudo symmetric ideals in a partially ordered ternary semigroup are introduced. We also studied some interesting properties prove that space is topologized.