TY - JOUR
AU - Chansuriya, Nagornchat
PY - 2022/06/29
Y2 - 2022/10/01
TI - Green’s Relations on a Ternary Monoid Hyp(2)
JF - Science & Technology Asia
JA - Sci Tech Asia
VL - 27
IS - 2
SE -
DO -
UR - https://ph02.tci-thaijo.org/index.php/SciTechAsia/article/view/241082
SP - 58-68
AB - <p>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 <img title="\tau" src="https://latex.codecogs.com/gif.latex?\tau" /> = (2) which is the set <em>Hyp</em>(2) of all hypersubstitutions of type <img title="\tau" src="https://latex.codecogs.com/gif.latex?\tau" /> = (2) together with the ternary operation [−, −, −] and identity element <img title="\sigma" src="https://latex.codecogs.com/gif.latex?\sigma" /><em><sub>id</sub></em> = <img title="\sigma" src="https://latex.codecogs.com/gif.latex?\sigma" /><sub><em>f (x1,x2)</em></sub>. 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 <img title="\tau" src="https://latex.codecogs.com/gif.latex?\tau" /> = (2) and describe the classes of elements of this monoid under Green’s relations <em>L<sup>T</sup> , R<sup>T</sup> ,D<sup>T</sup></em> and some of the<em> I<sup>T</sup></em> −class of elements. </p>
ER -