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

Let I , H , S , P , P _f be the usual operators on classes of algebras of the same type (P _f 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 \cal M =\langle H, S, P\rangle and by \cal M _f =\langle H, S, P _f \rangle the partially ordered monoids generated by {H, S, P} and by {H, S, P _f } respectively. The aim of this paper is to prove that \cal M is isomorphic to \cal M _f . October 29, 1999