We describe new types of normal forms for braid monoids, Artin– Tits monoids, and, more generally, all monoids in which divisibility has some convenient lattice properties (“locally Garside monoids”). We show that, in the case of braids, one of these normal forms turns out to coincide with the normal form introduced by Burckel and deduce that the latter can be computed easily. This approach lea...

This paper gives necessary and sufficient conditions for the restricted wreath product of two monoids to be finitely generated or finitely presented.

Based on different concepts to obtain a finer notion of language recognition via finite monoids we develop an algebraic structure called typed monoid. This leads to an algebraic description of regular and non regular languages. We obtain for each language a unique minimal recognizing typed monoid, the typed syntactic monoid. We prove an Eilenberg-like theorem for varieties of typed monoids as w...

We use ordered categories to study semidirect decompositions of finite ordered semigroups. We obtain ordered analogues of the derived category theorem and of the delay theorem. Next we prove that the ordered analogues of semilattices and of J -trivial monoids constitute local varieties, and we derive some decomposition theorems from these results. In [10], Pin and Weil initiated a study of the ...

valdis laan in [5] introduced an extension of strong flatness which is called weak pullback flatness. in this paper we introduce a new property of acts over monoids, called u-wpf which is an extension of weak pullback flatness and give a classification of monoids by this property of their acts and also a classification of monoids when this property of acts implies others. we also show that regu...

Abstract We describe structural and quantitative properties of type-dependent sets in monoids with suitable analytic structure, including simple monoids, introduced by Kaczorowski (Semigroup Forum 94:532–555, 2017. 10.1007/s00233-016-9778-9 ), formations, as defined Geroldinger Halter-Koch (Non-unique factorizations, Chapman Hall, Boca Raton, 2006. 10.1201/9781420003208 ). propose the notions r...

We prove that the pseudovariety DS, of all nite monoids each of whose regular D-classes is a subsemigroup, is local. (A pseudovariety (or variety) V is local if any category whose local monoids belong to V divides a member of V). The proof uses the \kernel theorem" of the rst two authors together with the description by P. Weil of DS as an iterated \block product". The one-sided analogues of th...

We work throughout in the category Cmd of commutative monoids. In other words, all the monoids we meet are commutative, and consequently we say 'monoid' in place of the longer 'commutative monoid'. However, occasionally we will emphasize the commu-tativity. Almost every monoid A we meet will be written multiplicatively, that is we write xy for the compound of x, y ∈ A. In places we write someth...

A group is Markov if it admits a prefix-closed regular language of unique representatives with respect to some generating set, and strongly Markov if it admits such a language of unique minimal-length representatives over every generating set. This paper considers the natural generalizations of these concepts to semigroups and monoids. Two distinct potential generalizations to monoids are shown...

Laan in (Ph.D Thesis, Tartu. 1999) introduced the principal weak form of Condition $(P)$ as Condition $(PWP)$ and gave some characterization of monoids by this condition of their acts. In this paper first we introduce Condition (G-PWP), a generalization of Condition $(PWP)$ of acts over monoids and then will give a characterization of monoids when all right acts satisfy this condition. We also ...