On the Partially Ordered Monoid Generated by the Operators H, S, P, Ps on Classes of Algebras

Let H, S, P be the standard operators on classes of algebras of the same type and Ps be the operator of closure under subdirect products. In this paper the monoid generated by class operators H, S, P, Ps and the corresponding partially ordered set are described. It turns out that there are 22 different operators such that every composition of H, S, P, Ps coincides with one of them. The semigroups (monoids) of operators H, S, P, Ps for the varieties of Boolean algebras, distributive lattices, unary algebras (of countable unary type), Abelian groups, and groups are also described