Our aim in this paper is to study the concept of stability for acts over monoids and in the process develop connections with flatness properties of acts and with some of the current techniques and construction used in the homological classification of monoids. We also present new proofs of some results relating to torsion free acts over monoids and to the embeddability of semigroup amalgams.
Dans cet article, nous introduisons la notion de semi-groupe fortement automatique, qui entraîne la notion d’automaticité des semi-groupes usuelle. On s’intéresse particulièrement aux semi-groupes de développements en base , pour lesquels on obtient un critère de forte automaticité.
This paper recalls some properties of a cyclic semigroup and examines cyclic subsemigroups in a finite ordered semigroup. We prove that a partially ordered cyclic semigroup has a spiral structure which leads to a separation of three classes of such semigroups. The cardinality of the order relation is also estimated. Some results concern semigroups with a lattice order.