Dominions, zigzags and epimorphisms for partially ordered semigroups

Morita invariants for partially ordered semigroups with local units

We study Morita invariants for strongly Morita equivalent partially ordered semigroups with several types of local units. These include the greatest commutative images, satisfying a given inequality and the fact that strong Morita equivalence preserves various sublattices of the lattice of ideals.

Probability Distributions on Partially Ordered Sets and Positive Semigroups

The algebraic structure ([0,∞), +, ≤), together with Lebesgue measure (and the usual topology), is the standard representation of time for a variety of probabilistic models. These include reliability theory and the aging of lifetime distributions, renewal processes, and Markov processes, to name just a few. The purpose of this monograph is to study probability models in which the standard repre...

On Morita equivalence of partially ordered semigroups with local units

We show that for two partially ordered semigroups S and T with common local units, there exists a unitary Morita context with surjective maps if and only if the categories of closed right Sand T posets are equivalent.

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 ...