ON DECOMPOSITIONS OF ORDERED SEMIGROUPS

Semidirect Product Decompositions of Ordered Groupoids and Inverse Semigroups

On fuzzy ordered semigroups

There are two equivalent de nitions of a fuzzy right ideal, fuzzy left ideal, fuzzy bi-ideal or fuzzy quasi-ideal f of an ordered semigroup (or a semigroup) S in the bibliography. The rst one is based on the fuzzy subset f itself, the other on the multiplication of fuzzy sets and the greatest fuzzy subset of S. Investigations in the existing bibliography are based on the rst de nition. The pres...

Decompositions of Differentiable Semigroups

A differentiable semigroup is a topological semigroup (5, *) in which 5 is a differentiable manifold based on a Banach space and the associative multiplication function * is continuously differentiable. If e is an idempotent element of such a semigroup we show that there is an open set U containing e so that there is a C retraction of U into the set of idempotents of S so that (x)<$(y) =...

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...

On representable ordered residuated semigroups

We show that the equational theory of representable lattice-ordered residuated semigroups is not finitely axiomatizable. We apply this result to the problem of completeness of substructural logics.