Ordered power ternary semigroups

We consider a power ternary semigroup [Formula: see text] associated with a ternary semigroup [Formula: see text] and study some properties of [Formula: see text] by using the corresponding properties of [Formula: see text]. After that we study the notion of ordered power ternary semigroup and our main aim is to establish some interconnection between the properties of a ternary semigroup [Formula: see text] and the associated ordered ternary semigroup [Formula: see text].

Ternary semigroups of topological transformations

A ternary semigroup is a nonempty set with a ternary operation which is associative. The purpose of the present paper is to give a characterization of open sets of finite-dimensional Euclidean spaces by ternary semigroups of pairs of homeomorphic transformations and extend to ternary semigroups certain results of L.M. Gluskin concerned with semigroups of homeomorphic transformations of finite-dimensional Euclidean spaces.

Ternary Menger Algebras: A Generalization of Ternary Semigroups

Let n be a fixed natural number. Menger algebras of rank n, which was introduced by Menger, K., can be regarded as the suitable generalization of arbitrary semigroups. Based on this knowledge, an interesting question arises: what a generalization of ternary semigroups is. In this article, we first introduce the notion of ternary Menger algebras of rank n, which is a canonical generalization of arbitrary ternary semigroups, and discuss their related properties. In the second part, we establish the so-called a diagonal ternary semigroup which its operation is induced by the operation on ternary Menger algebras of rank n and then investigate their interesting properties. Moreover, we introduce the concept of homomorphism and congruences on ternary Menger algebras of rank n. These lead us to study the quotient ternary Menger algebras of rank n and to investigate the homomorphism theorem for ternary Menger algebra of rank n with respect to congruences. Furthermore, the characterization of reduction of ternary Menger algebra into Menger algebra is presented.

Note on topological ternary semigroup

In this paper, we have discussed various topological properties of (Hausdörff) topological ternary semigroup and topological ternary group. We have proved that the Cartesian product of an arbitrary family of topological ternary semigroups is again a topological ternary semigroup. We have investigated the existence of identity and idempotent in a topological ternary semigroup and discussed a method to topologize a ternary semigroup (group) with a compatible topology using some family of pseudometrics. Finally, we have proved that a compact topological ternary semigroup contains a ternary subgroup.

KONDISI MINIMAL IDEAL KIRI TERURUT PADA SEMIGRUP TERNER TERURUT PARSIAL

Ternary semigroups 𝑇 is obtained from a nonempty set 𝑇 that given a mapping with a multiplication operation ternary that satisfied closed and associative properties. So, generally a ternary semigroup is an abstraction of a semigroup structure. Meanwhile, partially ordered ternary semigroups 𝑇 is an ordered semigroup 𝑇 that satisfies the properties for each 𝑎, 𝑏, 𝑐, 𝑑 ∈ 𝑇 if 𝑎 ≤ 𝑏 then (𝑎𝑐𝑑) ≤ (𝑏𝑐𝑑) and (𝑑𝑐𝑎) ≤ (𝑑𝑐𝑏). In a ternary semigroups there is also concept of left ideals. This study was conducted to examine the characteristics of ordered left ideals on partially ordered ternary semigroups. Furthermore, it will be discussed about the characteristics of minimal ordered left ideals on partially ordered semigroups.Keywords : Ternary Semigroups, Ordered Ternary Semigroups, Left Ideals, Ordered Left Ideals, Minimal of Ordered Left Ideals.

Global determinism of ternary semilattices

The global determinism of a ternary semigroup [Formula: see text] is the set of all nonempty subsets of [Formula: see text], denoted by [Formula: see text] equipped with the naturally defined multiplication. A class [Formula: see text] of ternary semigroups is said to be globally determined if any two members [Formula: see text] and [Formula: see text] of [Formula: see text] with isomorphic globals are themselves isomorphic i.e. [Formula: see text] implies that [Formula: see text] for any two ternary semigroups [Formula: see text] and [Formula: see text] in the class [Formula: see text]. In this paper, we mainly discuss that the class of all ternary semilattices are globally determined.

Regular Ordered Ternary Semigroups in Terms of Bipolar Fuzzy Ideals

Our main objective is to introduce the innovative concept of (α,ß)-bipolar fuzzy ideals and (α,ß)-bipolar fuzzy generalized bi-ideals in ordered ternary semigroups by using the idea of belongingness and quasi-coincidence of an ordered bipolar fuzzy point with a bipolar fuzzy set. In this research, we have proved that if a bipolar fuzzy set h = (S; hn, hp) in an ordered ternary semigroup S is the (∈,∈ ∨ q)-bipolar fuzzy generalized bi-ideal of S, it satisfies two particular conditions but the reverse does not hold in general. We have studied the regular ordered ternary semigroups by using the (∈,∈ ∨ q)-bipolar fuzzy left (resp. right, lateral and two-sided) ideals and the (∈,∈ ∨ q)-bipolar fuzzy generalized bi-ideals.

On Characterization of Open Sets in Euclidean Spaces

A ternary semigroup is a nonempty set T together with a ternary oper- ation [abc] satisfying the associative law [[abc] de] = [a [bcd] e] = [ab [cde]] for all a, b, c, d, e ε T. A map f between topological spaces X and Y is called open if the image of each set open in X is open in Y. The pur- pose of this paper is to give an abstract characterization of the ternary semigroups of open maps defined on open sets in Euclidean n-spaces.