ALL MAXIMAL COMPLETELY REGULAR SUBMONOIDS OF HypG(n)

Abstract

A generalized hypersubstitution of type τ = (n) is a mapping σ which maps the n-ary operation symbol f to the term σ(f) which does not necessarily preserve the arity. The set of all generalized hypersubstitutions of type τ = (n) together with a binary operation defined on this set and the identity hypersubstitution σid which maps f to the term f(x1, ..., xn) forms a monoid. Our motivation in this paper, is to determine all maximal completely regular submonoids of this monoid.