We prove that a language of a finitely generated free monoid is regular if and only if it satisfies the positive block pumping property. This gives a positive answer to a problem posed by Ehrenfeucht, Parikh, and Rozenberg [SIAM J. Comput., 10 (1981), pp. 536–541].

We prove a cancellation theorem for simple refinement monoids satisfying the weak comparability condition, first introduced by K.C. O’Meara in the context of von Neumann regular rings. This result is then applied to von Neumann regular rings and C∗-algebras of real rank zero via the monoid of isomorphism classes of finitely generated projective modules. Introduction Let M be an (abelian) monoid...

We introduce formal languages over infinite alphabets where words may contain binders. We define the notions of nominal language, nominal monoid, and nominal regular expressions. Moreover, we extend history-dependent automata (HD-automata) by adding stack, and study the recognisability of nominal languages.

We introduce formal languages over infinite alphabets where words may contain binders. We define the notions of nominal language, nominal monoid, and nominal regular expressions. Moreover, we extend history-dependent automata (HD-automata) by adding stack, and study the recognisability of nominal languages.

Let us suppose we are given an irreducible, Poncelet, pairwise regular monoid Ō. The goal of the present paper is to compute trivially stable equations. We show that Kummer’s conjecture is true in the context of polytopes. This leaves open the question of existence. The work in [5] did not consider the hyper-standard case.

Let R be a ring, M a right R-module and (S,≤) a strictly ordered monoid. In this paper we will show that if (S,≤) is a strictly ordered monoid satisfying the condition that 0 ≤ s for all s ∈ S, then the module [[MS,≤]] of generalized power series is a uniserial right [[RS,≤]] ]]-module if and only if M is a simple right R-module and S is a chain monoid.

We give a definition of the notion spherical varieties in world complex supervarieties with actions algebraic supergroups. A characterization affine is given which generalizes classical case. also explain some general properties monoid highest weights. Several examples are discussed that interesting their own right and highlight differences case, including regular representation, symmetric supe...

It is known that a number of algebraic properties of the braid groups extend to arbitrary finite Coxeter type Artin groups. Here we show how to extend the results to more general groups that we call Garside groups. Define a Gaussian monoid to be a finitely generated cancellative monoid where the expressions of a given element have bounded lengths, and where left and right lower common multiples...

The relation R̃ on a monoid S provides a natural generalisation of Green’s relation R. If every R̃-class of S contains an idempotent, S is left semiabundant; if R̃ is a left congruence then S satisfies (CL). Regular monoids, indeed left abundant monoids, are left semiabundant and satisfy (CL). However, the class of left semiabundant monoids is much larger, as we illustrate with a number of example...