The setting of this research is Bishop’s constructive mathematics. Following ideas of Chan and Shum, exposed in their famous paper “Homomorphisms of implicative semigroups”, we discuss the structure of implicative semigroups on sets with tight apartness. Moreover, we use anti-orders instead of partial orders. We study concomitant issues induced by existence of apartness and anti-orders giving s...

This paper studies FA-presentable structures and gives a complete classification of the finitely generated FA-presentable cancellative semigroups. We show that a finitely generated cancellative semigroup is FA-presentable if and only if it is a subsemigroup of a virtually abelian group.

with the norm ‖f‖Aq = ‖f‖L1 +‖f̂‖lq . Then Aq(G) is a commutative semisimple Banach algebra with maximal ideal space Γ , in which the set of trigonometric polynomials is dense [4]. The Ap-spaces have been studied in [1, 6]. If G is, in addition, a connected group, then its dual can be ordered; there exists a semigroup P ⊂ Γ such that P∩−P = {0}, P∪−P = Γ (see [5]), and we say that γ ∈ Γ is posit...

For an anti-congruence q we say that it is regular anti-congruence on semigroup (S,=, =, ·, α) ordered under anti-order α if there exists an antiorder θ on S/q such that the natural epimorphism is a reverse isotone homomorphism of semigroups. Anti-congruence q is regular if there exists a quasi-antiorder σ on S under α such that q = σ ∪ σ−1. Besides, for regular anti-congruence q on S, a constr...

This paper extends the notion of Compositional Equivalence for multiple networks developed by Breiger and Pattison (1986) by providing with an effective way to include actor attributes in their relational structures. The relevant characteristics acquired from the actors are integrated into a single partially ordered semigroup structure that relates both ties and actor attributes in the network ...

For a pseudovariety V of ordered semigroups, let S (V) be the class of sofic subshifts whose syntactic semigroup lies in V. It is proved that if V contains Sl− then S (V∗D) is closed for taking shift equivalent subshifts, and conversely, if S (V) is closed for taking conjugate subshifts then V contains LSl− and S (V) = S (V∗D). Almost finite type subshifts are characterized as the irreducible e...

The relative rank rank(S : U) of a subsemigroup U of a semigroup S is the minimum size of a set V ⊆ S such that U together with V generates the whole of S. As a consequence of a result by Sierpiński it follows that for U ≤ TX , the monoid of all self-maps of an infinite set X, rank(TX : U) is either 0, 1, 2 or uncountable. In this paper we consider the relative ranks rank(TX : OX), where X is a...

In case K is a division ring, the set S coincides with the set generated by the perfect squares as used by Szele. This follows easily from the identity xyx = (xy)2(y~1)2y, x, yEK*. If the domain of integrity K is ordered, say K* = P\J( — P), then for an extension L of K the ordering of K can be extended to an ordering of L if and only if TEL*, where T is the additive semigroup in L generated by...

The algebraic study of formal languages shows thatω-rational languages are exactly the sets recognizable by finite ω-semigroups. Within this framework, we provide a construction of the algebraic counterpart of the Wagner hierarchy. We adopt a hierarchical game approach, by translating the Wadge theory from the ω-rational language to the ω-semigroup context. More precisely, we first define a red...

S.B. Rao conjectured in 1971 that graphic degree sequences are well quasi ordered by a relation defined in terms of the induced subgraph relation[6]. In 2008, M. Chudnovsky and P. Seymour proved this long standing Rao’s Conjecture by giving structure theorems for graphic degree sequences[1]. In this paper, we prove and use a fairly simple semigroup lemma to give a short proof of the bounded deg...