A poset is said to be ω-chain complete if every countable chain in it has a least upper bound. It is known that every partially ordered set has a natural ω-completion. In this paper we study the ω-completion of partially ordered semigroups, and the topological action of such a semigroup on its ω-completion. We show that, for partially ordered semigroups, ω-completion and quotient with respect t...

When restricted to cost arrays possessing the sum Monge property, many combinatorial optimization problems with sum objective functions become signi cantly easier to solve. The more general algebraic assignment and transportation problems are similarly easier to solve given cost arrays possessing the corresponding algebraic Monge property. We show that Monge-array results for two sum-of-edge-co...

The setting of this article is Classical algebra and Bishop’s constructive algebra (the algebra based on the Intuitionistic logic). The Esakia’s concept in the classical mathematics of strongly isotone mapping between ordered sets is extended onto two different concepts of mappings: on the concept of weakly isotone and the concept of strongly reverse isotone mapping of relational systems. Some ...

When restricted to cost arrays possessing the sum Monge property, many combinatorial optimization problems with sum objective functions become significantly easier to solve. The more general algebraic assignment and transportation problems are similarly easier to solve given cost arrays possessing the corresponding algebraic Monge property. We show that Monge-array results for two sum-of-edge-c...

1. A. H. Clifford, Naturally totally ordered commutative semigroups, Amer. J. Math. 76(1954), 631-646. 2. , Totally ordered commutative semigroups, Bull. Amer. Math. Soc. 64 (1958), 305-316. 3. O. Holder, Die Axiome der Quantitât und die Lehre vom Mass, Ber. Verh. Sachs. Ges. Wiss. Leipzig Math.-Phys. Kl. 53 (1901), 1-64. 4. T. Tamura, Commutative nonpotent archimedean semigroup with cancellati...

In this paper we combine results from [1] and [3] in order to determine the relationship between the deficiency of a group G and the deficiency of a Rees matrix semigroup S over G; in particular, we investigate how the efficiency of S depends on the efficiency of G. We start by defining semigroup and group presentations. Let A be an alphabet. We denote by A the free semigroup on A consisting of...

Let 5 be a commutative semigroup. For a, b £5, we say that a divides b (or b is a multiple of a), and write a\b, if either a = b or ax = b for some x£5. We say that a properly divides b if a\b and b does not divide a. We call 5 archimedean if for all a, b £5, a divides some power of b. It is known that every commutative semigroup is uniquely expressible as a semilattice of archimedean semigroup...