Green’s Relations on a Ternary Monoid Hyp(2)

Abstract

The Green’s relations on a monoid of hypersubstitutions of type  = (2) were studied by K. Denecke and S. L. Wismath in [1]. Nevertheless, this study extends the similar concept to a ternary monoid of hypersubstitutions of type = (2) which is the set Hyp(2) of all hypersubstitutions of type = (2) together with the ternary operation [−, −, −] and identity element _id = _f (x1,x2). Some of the algebraic-structural properties of this monoid were studied by the author in [5]. The Green’s relations on a ternary semigroup were studied by Rabah Killil in [2]. In this paper, we apply the concept of Rabah Killil to a ternary monoid of hypersubstitutions of type = (2) and describe the classes of elements of this monoid under Green’s relations L^T , R^T ,D^T and some of the I^T −class of elements.