The Universal Theory of Ordered Equidecomposability Types Semigroups

The universal theory of ordered equidecomposability types semigroups

We prove that a commutative preordered semigroup embeds into the space of all equidecomposability types of subsets of some set equipped with a group action (in short, a full type space) if and only if it satisfies the following axioms: (i) (∀x,y)(x≤x+y); (ii) (∀x,y) ( (x≤y and y≤x)⇒x=y ) ; (iii) (∀x,y,u,v) ( (x+u≤y+u and u≤v)⇒x+v≤y+v ) ; (iv) (∀x,u,v) ( (x+u=u and u≤v)⇒x+v=v ) ; (v) (∀x,y)(mx≤m...

UNIVERSAL COMPACTIFICATIONS OF TRANSFORMATION SEMIGROUPS

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.

New types of intuitionistic fuzzy interior ideals of ordered semigroups

In many applied disciplines like computer science, coding theory and formal languages, the use of fuzzified algebraic structures play a remarkable role. In this paper, we introduced some new types of generalization of an intuitionistic fuzzy interior ideal, called (α, β)-intuitionistic interior ideals of an ordered semigroup S. The important milestone of this paper is to link the ordinary inter...

Regular ordered semigroups and intra-regular ordered semigroups in terms of fuzzy subsets

Let $S$ be an ordered semigroup. A fuzzy subset of $S$ is anarbitrary mapping   from $S$ into $[0,1]$, where $[0,1]$ is theusual interval of real numbers. In this paper,  the concept of fuzzygeneralized bi-ideals of an ordered semigroup $S$ is introduced.Regular ordered semigroups are characterized by means of fuzzy leftideals, fuzzy right ideals and fuzzy (generalized) bi-ideals.Finally, two m...

Ordered Categories and Ordered Semigroups