The purpose of this paper is to characterizeM -strongly solid monoids of generalized hypersubstitutions of type τ = (2) which is the extension of M -solid monoids of hypersubstitutions of the same type.

This paper gives a self-contained and complete proof of the isomorphism of freely generated monoids extracted from Temperley-Lieb algebras with monoids made of Kauffman’s diagrams. Mathematics Subject Classification (2000): 57M99, 20M05

This paper gives a self-contained and complete proof of the isomorphism of freely generated monoids extracted from Temperley-Lieb algebras with monoids made of Kauffman’s diagrams. Mathematics Subject Classification (2000): 57M99, 20M05

We give a short proof, using profinite techniques, that idempotent pointlikes, stable pairs and triples are decidable for the pseudovariety of aperiodic monoids. Stable pairs are also described for the pseudovariety of all finite monoids.

In this paper, we first consider n × n upper-triangular matrices with entries in a given semiring k. Matrices of this form with invertible diagonal entries form a monoid Bn(k). We show that Bn(k) splits as a semidirect product of the monoid of unitriangular matrices Un(k) by the group of diagonal matrices. When the semiring is a field, Bn(k) is actually a group and we recover a well-known resul...

We prove that monoids Mon〈a, b, c, d : ab = 0, ac = 1, db = 1, dc = 1 dab = 1, dab = 1, . . . , dab = 1〉 are congruence-free for all n ≥ 1. This provides a new countable family of finitely presented congruence-free monoids, bringing one step closer to understanding the Boone–Higman Conjecture. We also provide examples which show that finitely presented congruence-free monoids may have quadratic...

Let G be a digraph with n vertices and let A(G) be its adjacency matrix. A monic polynomial f (x) of degree at most n is called an annihilating polynomial of G if f (A(G)) = 0. G is said to be annihilatingly unique if it possesses a unique annihilating polynomial. Difans and diwheels are two classes of annihilatingly unique digraphs. In this paper, it is shown that the complete product of difan...

In this paper we pursue the study of the decidability of the dot-depth hierarchy. We give an effective lower bound for the dot-depth of an aperiodic monoid. The main tool for this is the study of a certain operation on varieties of finite monoids in terms of Mal’cev product. We also prove the equality of two decidable varieties which were known to contain all dot-depth two monoids. Finally, we ...

A monoid is special if it is presented by a set of relations of the form r = e. This paper investigates the problem of conjuacy in special monoids. After showing that the different concepts of conjugacy become identical in special monoids, which gives an affirmative answer to an open problem in 171, we prove that the conjugacy problem is decidable for some restricted classes of special monoids....