All intra-regular and relationship between some regular submonoids of Relhyp((m),(n))

Abstract

An algebraic system is a structure consisting of a nonempty set together with a sequence of operations and a sequence of relations on it. A relational hypersubstitution for algebraic systems is a mapping which maps any operation to a term and maps any relation to a relational term preserving its arities. The set of all such relational hypersubstitutions for algebraic systems forms a monoid. In this paper, we characterize the set of all intra-regular elements of the monoid of all relational hypersubstitutions of type ((m), (n)) and show that the set of all intra-regular elements, set of all left (right) regular elements and the set of all completely regular elements of Relhyp((m), (n)) are the same.