The aim of this paper is to study certain quasivarieties of left ample monoids. Left ample monoids are monoids of partial one–one mappings of sets closed under the operation α 7→ αα−1. The idempotents of a left ample monoid form a semilattice and have a strong influence on the structure of the monoid; however, a left ample monoid need not be inverse. Every left ample monoid has a maximum right ...

We give a characterization of primary ideals of finitely generated commutative monoids and in the case of finitely generated cancellative monoids we give an algorithmic method for deciding if an ideal is primary or not. Finally we give some properties of primary elements of a cancellative monoid and an algorithmic method for determining the primary elements of a finitely generated cancellative ...

A. Problems involving chains of irreducible factorizations in atomic integral domains and monoids have been the focus of much recent literature. If S is a commutative cancellative atomic monoid, then the catenary degree of S (denoted c(S )) and the tame degree of S (denoted t(S )) are combinatorial invariants of S which describe the behavior of chains of factorizations. In this note, we ...

We prove that left cancellative right hereditary monoids satisfying the dedekind height property are precisely the Zappa-Szép products of free monoids and groups. The ‘fundamental’ monoids of this type are in bijective correspondence with faithful self-similar group actions. 2000 AMS Subject Classification: 20M10, 20M50. 1 A class of left cancellative monoids This paper develops some ideas that...

Problems involving chains of irreducible factorizations in atomic integral domains and monoids have been the focus of much recent literature. If S is a commutative cancellative atomic monoid, then the catenary degree of S (denoted c(S)) and the tame degree of S (denoted t(S)) are combinatorial invariants of S which describe the behavior of chains of factorizations. In this note, we describe met...

Assume that G is a group of fractions of a cancellative monoid where lower common multiples exist and divisibility has no infinite descending chain. Then G is torsion free. The result applies in particular to all finite Coxeter type Artin groups. Finding an elementary proof for the fact that Artin’s braid groups are torsion free has been reported to be a longstanding open question [9]. The exis...

In this paper we introduce R-right (left), L-left (right) cancellative and weakly R(L)-cancellative semigroups and will give some equivalent conditions for completely simple semigroups, (completely) regular right (left) cancellative semigroups, right (left) groups, rectangular groups, rectangular bands, groups and right (left) zero semigroups according to R-right (left), L-left (right) and weak...

It is well known that automatic groups can be characterized using geometric properties of their Cayley graphs. Along the same line of thought, we provide a geometric characterization of automatic monoids. This involves working with a slightly strengthened definition of an automatic monoid which is still a proper generalization of the concept of an automatic group. The two definitions coincide i...

In this note we will show that the dilation result obtained for fractional skew monoid rings, in the case of a cancellative left Ore monoid S acting on a unital ring A by corner isomorphisms, holds in full generality. We apply this result to the context of semigroup C∗-crossed products.

AmonoidM is called surjunctive if every injective cellular automata with finite alphabet over M is surjective. We show that all finite monoids, all finitely generated commutative monoids, all cancellative commutative monoids, all residually finite monoids, all finitely generated linear monoids, and all cancellative one-sided amenable monoids are surjunctive. We also prove that every limit of ma...