ORDERED CATEGORIES AND ORDERED SEMIGROUPS

Ordered Categories and Ordered Semigroups

Ordered categories and ordered semigroups

We use ordered categories to study semidirect decompositions of finite ordered semigroups. We obtain ordered analogues of the derived category theorem and of the delay theorem. Next we prove that the ordered analogues of semilattices and of J -trivial monoids constitute local varieties, and we derive some decomposition theorems from these results. In [10], Pin and Weil initiated a study of the ...

Finite semigroups as categories, ordered semigroups or compact semigroups

The results presented in this section are a good illustration of the following quotation of Marshall Stone [34]: ’A cardinal principle of modern mathematical research may be stated as a maxim: “One must always topologize” ’. Varieties of finite semigroups are a good example where Stone’s principle was applied successfully. Recall that a variety of semigroups is a class of semigroups closed unde...

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...

Characterizing Ordered Bi-Ideals in Ordered Γ-Semigroups

The notion of a &Gamma-semigroup was introduced by Sen [8] in 1981. We can see that any semigroup can be considered as a &Gamma-semigroup. The aim of this article is to study the concept of (0-)minimal and max- imal ordered bi-ideals in ordered &Gamma-semigroups, and give some charac- terizations of (0-)minimal and maximal ordered bi-ideals in ordered &Gamma- semigroups analogous to the charact...