Vol. 83, No. 1, 1979

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A primeness property for central polynomials

Amitai Regev

Vol. 83 (1979), No. 1, 269–271
Abstract

In this note we prove an anolog of Amitsur’s theorem for central polynomials.

Theorem. Let F be an infinite field, f(x) = f(x1,,xr), g(x) = g(xr+1,,xs) two noncommutative polynomials in disjoint sets of variables. Assume that f(x1,,xr) g(xr+1,,xs) is central but not an identity for Fk. Then both f(x) and g(x) are central polynomials for Fk.

Mathematical Subject Classification
Primary: 16A38, 16A38
Secondary: 16A42
Milestones
Received: 9 August 1978
Published: 1 July 1979
Authors
Amitai Regev