In this paper, it is proven that a semigroup is regular and RGC_n-commutative if, and only if, it is a spined product of a commutative Clifford semigroup and a right regular band

We show that for every $n\in\mathbb{N}$, the direct product of the cyclic semigroup of order $n$ and period $1$ and the left zero semigroup $2^\mathfrak{c}$ has copies in $\beta\mathbb{N}$.

Let S be an ordered semi group. A fuzzy subset of S is an arbitrary mapping from S into [0,1], where [0,1] is the usual interval of real numbers. In this paper, the concept of fuzzy generalized bi-ideals of an ordered semi group S is introduced. Regular ordered semi groups are characterized by means of fuzzy left ideals, fuzzy right ideals and fuzzy (generalized) bi-ideals. Finally, two main theorems which characterize regular ordered semi groups and intraregular ordered semi groups in terms of fuzzy left ideals, fuzzy right ideals, fuzzy bi-ideals or fuzzy quasi-ideals are given. The paper shows that one can pass from results in terms of fuzzy subsets in semi groups to ordered semi groups. The corresponding results of unordered semi groups are also obtained.

In this note we study the transformation semigroup (X,S), where S is a finite union of its subSemigroups

We extend the notion of semigroup compactification to the class of transformation Semigroups, and determine the compactifications which are universal with respect to some topological properties.