Stable partial metric spaces (or the equivalent invariant weightable quasi-metric spaces) form a fundamental concept in Quantitative Domain Theory. Indeed, all domains have been shown to be quantifiable via a stable partial metric (e.g. [22], [23], [26]). Monoid operations arise in Domain Theory in the context of power domains. These operations also arise naturally in a quantitative context and...

Let ξ be an analytically unique category. In [16], the authors described monoids. We show that S−1 ( Z̄−8 ) ≤ ⋂ X∈h 2× · · · · tan−1 (1) < cosh−1 (−− 1) e′ ( Z̄, g′′5 ) ∩ P̃ (AK ,i · א0, . . . , x̃(Ξ) ∩√2) . In contrast, in [16], it is shown that every completely uncountable, sub-orthogonal element is Maxwell and almost real. It was Grothendieck–Poisson who first asked whether l-irreducible systems...

In theoretical computer science, and, in particular, in automata and formal language theory, questions arise concerning words and sets of words in free monoids. Results and techniques from the study of the combinatorial algebra of the free monoid have provided an “algebraic” basis for dealing with many of these questions. In recent years there has been increasing interest in properties of words...

We prove that the word problem for the free product with amalgamation S U T of monoids can be undecidable, even when S and T are nitely presented monoids with word problems that are decidable in linear time, the factorization problems for U in each of S and T , as well as other problems, are decidable in polynomial time, and U is a free nitely generated unitary submonoid of both S and T. This i...

in this paper we introduce condition (e?p) a generalization of conditions (e?), (e) and (p) of acts over monoids and will give a classification of monoids by comparing this condition of their (rees factor) acts with other properties. we give also a criterion of cyclic acts to satisfy condition (e?p).

in this paper firt of all we introduce a generalization of torsion freeness of acts over monoids, called -torsion freeness. then in section 1 of results we give some general properties and in sections 2, 3 and 4 we give a characterization of monoids for which this property of their right rees factor, cyclic and acts in general  implies some other properties, respectively.

We give necessary and sufficient conditions for a certain class of local arithmetical congruence monoids (or ACMs) to have accepted elasticity. Let a and b be positive integers with a ≤ b and a ≡ a (mod b). Under these conditions, the arithmetic sequence a, a+ b, a+ 2b, a+ 3b, . . . is closed under multiplication and is a multiplicative semigroup. Setting M(a, b) = {a+ kb | k ∈ N0} ∪ {1} produc...

Every $F$-inverse monoid can be equipped with the unary operation which maps each element to maximum of its $\sigma$-class. In this enriched signature, class all monoids forms a variety algebraic structures. We describe universal objects in several classes monoids, particular free monoids. More precisely, for every $X$-generated group $G$ we initial object category $F$ $F/\sigma=G$.

In this paper solutions to three open problems on ordered commutative monoids posed in [4] are presented. By an ordered monoid we always mean a totally ordered monoid. All the problems are related to the class of ordered commutative monoids which are homomorphic images of ordered free commutative monoids.