Idempotents, band and Green's relations on ternary semigroups

Abstract

This paper is for one part a generalization of some results obtained by Miyuki Yamada [20] in the case of binary semigroups to ternary semigroups. We prove analogous of almost all the results previously cited. We prove in particular that the set of the idempotents in regular ternary semigroup is a band (that is, a semigroup). In a second part we continue our investigations started in [13; 14] on these semigroups, as on the structure of the set E(S) of idempotents of the ternary semigroup S. The particular case of ternary inverse semigroup has been studied and a relationship between the existence of idempotents and the inverse elements has been caracterized. The documents [5]; [9] and [10] have been intensively used. We asked two questions and the answer for the second one will be the subject of a forcoming paper. We use many references in our work the most important are those used as bibliography.