The notions of uni-soft semigroups, uni-soft left (right) ideals and uni-soft quasi ideals are introduced, and related properties are investigated. Characterizations of uni-soft semigroups, uni-soft left (right) ideals and uni-soft quasi ideals are discussed. A regular semigroup is characterized by the notion of a uni-soft quasi ideal.

We investigate the results of a partially ordered ternary semigroup containing right bases and characterize when non-empty subset is base. Moreover, we give characterization base to be subsemigroup show that have same cardinality. Finally, complement union all maximal proper left ideal.

We generalize results concerning C0-semigroups on Banach lattices to a setting of ordered Banach spaces. We prove that the generator of a disjointness preserving C0-semigroup is local. Some basic properties of local operators are also given. We investigate cases where local operators generate local C0-semigroups, by using Taylor series or Yosida approximations. As norms we consider regular norm...

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 ...

We study C*-algebras associated with subsemigroups of groups. For a large class of such semigroups including positive cones in quasi-lattice ordered groups and left Ore semigroups, we describe the corresponding semigroup C*algebras as C*-algebras of inverse semigroups, groupoid C*-algebras and full corners in associated group crossed products. These descriptions allow us to characterize nuclear...

Semigroups with an additional unary operation called a (right) closure are investigated. These “closure semigroups” may be viewed as (not necessarily regular) generalisations of inverse semigroups, and several powerful structural aspects of inverse semigroup theory are shown to extend naturally to some important classes of closure semigroups. These include representations as partial transformat...

For a nonempty set X, let T(X) be the total transformation semigroup on X. In this paper, we consider subsemigroups of which are defined by T(X,Y) ={α∈T(X):Xα⊆Y}andS(X,Y)={α∈T(X):Yα⊆Y} where Y is non-empty subset We characterize left regular and right elements both S(X,Y). Moreover, necessary sufficient conditions for S(X,Y) to given. These results then applied determine numbers in finite