In this paper, for each positive integer m, we associate with a finite monoid S0 and m finite commutative monoids S1,..., Sm, a product ◊m(Sm,..., S1, S0) . We give a representation of the free objects in the pseudovariety ◊m(Wm,..., W1, W0) generated by these (m + 1)-ary products where Si ∈ Wi for all 0 ≤ i ≤ m. We then give, in particular, a criterion to determine when an identity holds in ◊m...

In this paper we introduce condition (E?P) a generalization of Conditions (E?), (E) and (P) of acts over monoids and will give a classification of monoids by comparing this condition of their (Rees factor) acts with other properties. We give also a criterion of cyclic acts to satisfy Condition (E?P).

In this article we give a characterization of monoids for which torsion freeness, ((principal) weak, strong) flatness, equalizer flatness or Condition (E) of finitely generated and (mono) cyclic acts and Condition (P) of finitely generated and cyclic acts implies regularity. A characterization of monoids for which all (finitely generated, (mono) cyclic acts are regular will be given too. We als...

We associate a modal operator with each language belonging to a given class of regular languages and use the (reverse) wreath product of monoids with distinguished generators to characterize the expressive power of the resulting logic.

This paper gives decidable conditions for when a nitely generated subgroup of a free group is the fundamental group of a Sch utzenberger automaton corresponding to a monoid presentation of an inverse monoid. Also, generalizations are given to speciic types of inverse monoids as well as to monoids which are \nearly inverse." This result has applications to computing membership for inverse monoid...

It is shown that the multiplicative monoids of Temperley-Lieb algebras are isomorphic to monoids of endomorphisms in categories where an endofunctor is adjoint to itself. Such a self-adjunction is found in a category whose arrows are matrices, and the functor adjoint to itself is based on the Kronecker product of matrices. Thereby one obtains a representation of braid groups in matrices, which,...

We consider the property of unique parallel decomposition modulo branching and weak bisimilarity. First, we show that infinite behaviours may fail to have parallel decompositions at all. Then, we prove that totally normed behaviours always have parallel decompositions, but that these are not necessarily unique. Finally, we establish that weakly bounded behaviours have unique parallel decomposit...

— 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...

It is shown that the multiplicative monoids of Brauer’s centralizer algebras generated out of the basis are isomorphic to monoids of endomorphisms in categories where an endofunctor is adjoint to itself, and where, moreover, a kind of symmetry involving the self-adjoint functors is satisfied. As in a previous paper, of which this is a companion, it is shown that such a symmetric self-adjunction...