On the Partially Ordered Semigroup Generated by the Class Operators I, R, H, S, P

Abstract

Let I, H, S, P be the usual class operators on universal algebras. For a class script K sign of universal algebras of the same type, let R(script K sign) be the class of all algebras isomorphic to a retract of a member of script K sign and let R denote the corresponding class operator. In this paper the semigroup generated by class operators I, R, H, S, P and the corresponding partially ordered set are described. Also the standard semigroups of the above operators are determined for some varieties.