Malaysian Journal of Mathematical Sciences, May 2019, Vol. 13, No. 2
On Ternary Monoid of Hypersubstitutions of Type \(\tau =(n)\)
Chansuriya, N.
Corresponding Email: nagornchat.c@sciee.kmutnb.ac.th
Received date: 15 March 2017
Accepted date: 18 April 2019
Abstract:
A ternary monoid of hypersubstitutions of type \(\tau =(n)\) is the set \(Hyp(n)\) of all hypersubstitutions of type \(\tau =(n)\) with a ternary operation which satisfies the associative law, and has the identity element \(\sigma_{id}\) . For \(n=2\) , the idempotent and regular elements, the ideals of submonoids and some algebraic-properties of this monoid were studied by author. In this present paper, we study the algebraic-structural properties of \(Hyp(n)\), \(n>2\) and characterize the idempotent and regular elements. In particular, we describe the relationships between some submonoids of this monoid under the ideal of this submonoids.
Keywords: hypersubstitutions, ternary monoid, ternary ideal
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