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ON THE NUMBER OF POLYNOMIALS OF AN IDEMPOTENT ALGEBRA, II

The proof starts in §2 where a lemma of K. Urbanik is modified to show that the proof splits naturally into three cases. §§3 and 4 handle the first two cases. In §5 the third case is analyzed and it is proved that it splits into two further cases that are settled in §§6 and 7. In each of these sections examples are provided that the case under consideration is not void. For the undefined concepts and basic results the reader is referred to [2]. Examples of algebras satisfying the conditions of the Theorem abound. On a two element Boolean algebra {0, 1} the operation (x A y) V (y A z) V (z A x) defines such an algebra.