In part I of this
paper a conjecture was formulated according to which, with a few obvious
exceptions, the sequence ⟨pn(U)⟩ of an idempotent algebra is eventually strictly
increasing. In this paper this conjecture is verified for idempotent algebras
satisfying p2(U) = 0,pa(U) > 0, and p4(U) > 0. In fact, somewhat more is
proved:
Theorem. Let U 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
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