Strongly compatible total orders on free monoids.
Structure and embedding theorems for unique normal decomposition lattices
Structure of partially ordered cyclic semigroups
This paper recalls some properties of a cyclic semigroup and examines cyclic subsemigroups in a finite ordered semigroup. We prove that a partially ordered cyclic semigroup has a spiral structure which leads to a separation of three classes of such semigroups. The cardinality of the order relation is also estimated. Some results concern semigroups with a lattice order.
Subtraction semigroups
A subtraction semigroup is a semigroup with a further operation "" added, called subtraction and satisfying certain axioms. The paper concerns a problem by B. M. Schein concerning the structure of multiplication in a subtraction semigroup.
Sur les ...-bandes finies et les demigroupes totalement ordonnés ...-simples.
Sur les bandes réticulées.
Sur les demi-groupes réticulés et les O-demi-groupes.
Sur les demi-groupes totalement ordonnés -simples
Sur les groupoïdes-treillis
Sur les o-bandes.
The associativity equation revisited.
The chain of right simple semigroups in ordered semigroups
The duality between lattice-ordered monoids and ordered topological spaces.
The embedding of an ordered semigroup in a simple one with identity.
The Embedding of an Ordered Semigroup in an Ordered group via the Quotient Condition
The embedding of an ordered semigroup into an le-semigroup.
The functional equation f(xy) = ff(x) xy ff(y) in a partially ordered monoid.
The globals of pseudovarieties of ordered semigroups containing and an application to a problem proposed by Pin
Given a basis of pseudoidentities for a pseudovariety of ordered semigroups containing the 5-element aperiodic Brandt semigroup , under the natural order, it is shown that the same basis, over the most general graph over which it can be read, defines the global. This is used to show that the global of the pseudovariety of level of Straubing-Thérien’s concatenation hierarchy has infinite vertex rank.
The globals of pseudovarieties of ordered semigroups containing B2 and an application to a problem proposed by Pin
Given a basis of pseudoidentities for a pseudovariety of ordered semigroups containing the 5-element aperiodic Brandt semigroup B2, under the natural order, it is shown that the same basis, over the most general graph over which it can be read, defines the global. This is used to show that the global of the pseudovariety of level 3/2 of Straubing-Thérien's concatenation hierarchy has infinite vertex rank.
The Ideal extensions of ordered semigroups