On Naturally Ordered Abundant Semigroups with an Adequate Monoid Transversal

On Rees Matrix Representations of Abundant Semigroups with Adequate Transversals

The concepts of ∗-relation of a (Γ-)semigroup and Γ̄-adequate transversal of a (Γ-)abundant semigroup are defined in this note. Then we develop a matrix type theory for abundant semigroups. We give some equivalent conditions of a Rees matrix semigroup being abundant and some equivalent conditions of an abundant Rees matrix semigroup having an adequate transversal. Then we obtain some Rees matrix...

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...

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.

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 ...