Natural partial ordering on E(HypG(2))

Abstract

The concept of generalized hypersubstitutions was introduced by S. Leeratanavalee and K. Denecke as a way of making precise the concepts of strong hyperidentity and M-strong hyperidentity. The set HypG(2) of all generalized hypersubstitutions of type τ = (2) forms a monoid. All idempotent and regular elements in the monoid of all generalized hypersubstitutions of type τ = (2) were studied by W. Puninagool and S. Leeratanavalee. In this paper, we determine all primitive idempotent elements of this monoid and characterize the natural partial ordering on the set of all idempotent of this monoid. © 2013 World Scientific Publishing Company.