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...

Following Buchberger's approach to computing a Grr obner basis of a polynomial ideal in polynomial rings, a completion procedure for nitely generated right ideals in ZH] is given, where H is an ordered monoid presented by a nite, convergent semi{Thue system ((; T). Taking a nite set F ZH] we get a (possibly innnite) basis of the right ideal generated by F , such that using this basis we have un...

There exist a number of results proving that for certain classes of interacting particle systems in population genetics, mutual invadability of types implies coexistence. In this paper we prove a sort of converse statement for a class of one-dimensional cancellative systems that are used to model balancing selection. We say that a model exhibits strong interface tightness if started from a conf...

Cancellative dimer algebras on a torus have many nice algebraic and homological properties. However, these properties disappear for higher genus surfaces. We consider new class of quiver surfaces, called 'geodesic ghor algebras', that reduce to cancellative torus, yet continue These exhibit rich interplay between their central geometry the topology surface. show (nontrivial) geodesic do in fact...

Let Zn be the finite cyclic group of order n and S ⊆ Zn. We examine the factorization properties of the Block Monoid B(Zn, S) when S is constructed using a method inspired by a 1990 paper of Erdős and Zaks. For such a set S, we develop an algorithm in Section 2 to produce and order a set {Mi} i=1 which contains all the non-primary irreducible Blocks (or atoms) of B(Zn, S). This construction yie...

The following problem is considered: when can the action of a cancellative semigroup S on a set be extended to a simply transitive action of the universal group of S on a larger set.

we prove that if $m$ is a monoid and $a$ a finite set with more than one element‎, ‎then the residual finiteness of $m$ is equivalent to that of the monoid consisting of all cellular automata over $m$ with alphabet $a$‎.