On the number of polynomials of an idempotent algebra. II
George Grätzer, J. Płonka · Pacific Journal of Mathematics · 1973
In part I of this paper a conjecture was formulated according to which, with a few obvious exceptions, the sequence (Pn(&)} of an idempotent algebra is eventually strictly increasing.In this paper this conjecture is verified for idempotent algebras satisfying p 2 QX) -0, p z QX) > 0, and p*QX) > 0. In fact, somewhat more is proved: THEOREM.Let It be an idempotent algebra with no essentially binary polynomial and with essentially ternary and quaternary polynomials.Then the sequence is strictly increasing, that is, for all n ^ 2 PnQX) + 1 £ Pn+l(U) .