Sur les demi-groupes reticules et les o-demi-groupes |
| |
| Authors: | Thérèse Merlier |
| |
| Affiliation: | (1) Faculté des Sciences de Paris, Paris, France;(2) Present address: 15, Boulevard de la République, 92-Fontenay-aux-roses, France |
| |
| Abstract: | A necessary and sufficient condition is given in order that a lattice-ordered semigroup admit a totally ordered ?-homomorphic image (Theorem 1). This permits us to give (Theorem 2) a necessary and sufficient condition that a lattice-ordered semigroup be representable, that is, that it be ?-isomorphic to a subdirect product of totally ordered semigroups, thereby solving a problem posed by L. Fuchs ([2], p. 289). We also establish a necessary and sufficient condition that a semigroup be an o-semigroup, that is, that it admit a structure of totally ordered semigroup (Theorem 3). |
| |
| Keywords: | |
| 本文献已被 SpringerLink 等数据库收录！ |
|
