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

Authors

  • Nagornchat Chansuriya Faculty of Science, Energy and Environment, King Mongkut’s University of Technology North Bangkok, Rayong 21120, Thailand

Keywords:

Green’s relations, Hypersubstitutions, Ternary monoid

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 gif.latex?\tau = (2) which is the set Hyp(2) of all hypersubstitutions of type gif.latex?\tau = (2) together with the ternary operation [−, −, −] and identity element gif.latex?\sigmaid = gif.latex?\sigmaf (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 gif.latex?\tau = (2) and describe the classes of elements of this monoid under Green’s relations LT , RT ,DT and some of the IT −class of elements. 

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Published

2022-06-29

How to Cite

Chansuriya, N. (2022). Green’s Relations on a Ternary Monoid Hyp(2). Science & Technology Asia, 27(2), 58–68. Retrieved from https://ph02.tci-thaijo.org/index.php/SciTechAsia/article/view/241082

Issue

Section

Physical sciences