By constructions in monoid and group theory we exhibit an adjunction between the category of partially ordered monoids and lazy monoid homomorphisms, and the category of partially ordered groups and group homomorphisms, such that the unit of the adjunction is injective. We also prove a similar result for sets acted on by monoids and groups. We introduce the new notion of lazy homomorphism for a...

For a given reachable automaton A, we prove that the (state-)endomorphism monoid End(A) divides its characteristic monoid M(A). Hence so does its (state-)automorphism group Aut(A), and, for finite A, Aut(A) is a homomorphic image of a subgroup of the characteristic monoid. It follows that in the presence of a (state-) automorphism group G of A, a finite automaton A (and its transformation monoi...

We describe Green’s relations on the partition monoid, two of its submonoids, and the related Jones and Brauer monoids. Key Words: partition monoid, Jones monoid, ideal structure 2000 Mathematics Subject Classi…cation: 20M20 1 The partition monoid and some submonoids The elements of the partition monoid Pn [5, 8, 9] are equivalence classes of graphs on a vertex set n [ n0 = f1; 2; :::ng [ f10; ...

Let $R$ be a unitary ring with an endomorphism $σ$ and $F∪{0}$ be the free monoid generated by $U={u_1,…,u_t}$ with $0$ added, and $M$ be a factor of $F$ setting certain monomial in $U$ to $0$, enough so that, for some natural number $n$, $M^n=0$. In this paper, we give a sufficient condition for a ring $R$ such that the skew monoid ring $R*M$ is quasi-Armendariz (By Hirano a ring $R$ is called...

— 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...