Vol. 32, No. 3, 1970

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On the number of polynomials of an idempotent algebra. I

George Grätzer and J. Płonka

Vol. 32 (1970), No. 3, 697–709
Abstract

This paper deals with the number pn(A) of essentially n-ary polynomials of an idempotent universal algebra A. Under the condition that there is a commutative binary polynomial it is proved that pn+1(A) pn(A) + (n1), provided pn(A)1. If is also associative this inequality is improved to

pn+1(A ) ≧ pn(A)+ 1 + max{pn(A ),n + 1}.

Mathematical Subject Classification
Primary: 08.30
Milestones
Received: 28 July 1969
Revised: 4 November 1969
Published: 1 March 1970
Authors
George Grätzer
J. Płonka