We characterize, in terms of elementary properties, the abelian monoids which are direct limits of finite direct sums of monoids of the form ðZ=nZÞ t f0g (where 0 is a new zero element), for positive integers n. The key properties are the Riesz refinement property and the requirement that each element x has finite order, that is, ðnþ 1Þx 1⁄4 x for some positive integer n. Such monoids are neces...

Resumen. A partir de la implementación de dos bases de datos a priori independientes la una de la otra (libros virtuales y webs de interés para la comunidad universitaria), el Servicio de Bibliotecas y Documentación de la UPC se plantea el proyecto de integración de los distintos servicios que ofrece a través de su sede web mediante un esquema más amplio de bases de datos relacionales vinculada...

In this article we study a class of monoids that includes Garside monoids, and give a simple combinatorial proof of a formula for the formal sum of all elements of the monoid. This leads to a formula for the growth function of the monoid in the homogeneous case, and can also be lifted to a resolution of the monoid algebra. These results are then applied to known monoids related to Coxeter syste...

In this paper we present general techniques for characterising minimal and maximal semigroup topologies on the endomorphism monoid End(A) of a countable relational structure A. As applications, show that monoids several well-known structures, including random graph, directed partial order, possess unique Polish topology. every case topology is subspace induced by usual Baire space NN. We also m...

Linking diagrams with path composition are ubiquitous, for example: Temperley-Lieb and Brauer monoids, Kelly-Laplaza graphs for compact closed categories, and Girard’s multiplicative proof nets. We construct the category Link = Span(iRel), where iRel is the category of injective relations (reversed partial functions) and show that the aforementioned linkings, as well as Jones-Martin partition m...

In algebraic terms, the insertion of $n$-powers in words may be modelled at the language level by considering the pseudovariety of ordered monoids defined by the inequality $1\le x^n$. We compare this pseudovariety with several other natural pseudovarieties of ordered monoids and of monoids associated with the Burnside pseudovariety of groups defined by the identity $x^n=1$. In particular, we a...

The finite embeddability property (FEP) for integral, commutative residuated ordered monoids was established by W. J. Blok and C. J. van Alten in 2002. Using Higman’s finite basis theorem for divisibility orders we prove that the assumptions of commutativity and associativity are not required: the classes of integral residuated ordered monoids and integral residuated ordered groupoids have the ...