Partially Ordered Monoids Generated by Operators H , S , P , and by H , S , P f Are

Let I , H , S , P , Pf be the usual operators on classes of algebras of the same type (Pf for filtered products). The partially ordered monoid generated by the operators H , S , P with respect to composition of operators, I as an identity element, and a natural ordering between operators is described by Pigozzi (Algebra Universalis 2 (1972), 346–353). Let us denote by M = 〈H,S, P 〉 and by Mf = 〈H,S, Pf 〉 the partially ordered monoids generated by {H,S, P} and by {H,S, Pf} respectively. The aim of this paper is to prove that M is isomorphic to Mf .