Totally ordered commutative semigroups

Totally Ordered Commutative Semigroups

Let 5( + , < ) be a system consisting of a set S endowed with an associative binary operation + and a total ( = linear = simple) order relation < . The composition + and the relation < may be connected by either or both of the following conditions. MC (Monotone Condition). If a and b are elements of 5 such that ax+y ...

Ordered Commutative Semigroups of the Second Kind1

By an ordered commutative semigroup of the first kind (abbreviated "o.c.s.I") we mean a system 5(o, <) consisting of a set 5 endowed with a binary operation o and a binary relation < such that the following axioms are satisfied. I. S is a commutative semigroup with respect to o, i.e. the associative law, a o (b o c) = (a o b)o c, and the commutative law, a o b = b o a, hold (a, b, c in S). II. ...

Ordered Categories and Ordered Semigroups

Varieties of Commutative Semigroups

In this paper, we describe all equational theories of commutative semigroups in terms of certain well-quasi-orderings on the set of finite sequences of nonnegative integers. This description yields many old and new results on varieties of commutative semigroups. In particular, we obtain also a description of the lattice of varieties of commutative semigroups, and we give an explicit uniform sol...

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 ...