— Relational morphisms betweenfinite monoids (a notion due to Tilson) are used to study the effect certain opérations on recognizabie sets have on the syntactic monoids ofthose sets. This leads to concise proofs ofa number ofknown results concerning the product opération, and a new resuit concerning the star opération. Résumé. — On utilise les morphismes relationnels (dus à Tilson) pour étudier...

We construct certain monoids, called tied monoids. These monoids result to be semidirect products finitely presented and commonly built from braid groups their relatives acting on of set partitions. The nature our indicate that they should give origin new knot algebras; indeed, include the monoid singular monoid, which were used, respectively, polynomial invariants for classical links links. Co...

in (golchin a. and rezaei p., subpullbacks and flatness properties of s-posets. comm. algebra. 37: 1995-2007 (2009)) study was initiated of flatness properties of right -posets  over a pomonoid  that can be described by surjectivity of  corresponding to certain (sub)pullback diagrams and new properties such as  and  were discovered. in this article first of all we describe po-flatness propertie...

This paper concerns the monoid Hecke algebras H introduced by Louis Solomon. We determine explicitly the unities of the orbit algebras associated with the two-sided action of the Weyl group W . We use this to: 1. find a description of the irreducible representations of H, 2. find an explicit isomorphism between H and the monoid algebra of the Renner monoid R, 3. extend the Kazhdan-Lusztig invol...

We investigate the relationship between regular languages and syntactic monoid size. In particular, we consider the transformation monoids of n-state (minimal) deterministic finite automata. We show tight upper bounds on the syntactic monoid size, proving that an nstate deterministic finite automaton with singleton input alphabet (input alphabet with at least three letters, respectively) induce...