A primeness property for central polynomials

Amitai Regev

Vol. 83 (1979), No. 1, 269–271

DOI: 10.2140/pjm.1979.83.269

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,⋯,x_r), g(x) = g(x_r+1,⋯,x_s) two noncommutative polynomials in disjoint sets of variables. Assume that f(x₁,⋯,x_r) ⋅g(x_r+1,⋯,x_s) is central but not an identity for F_k. Then both f(x) and g(x) are central polynomials for F_k.

Mathematical Subject Classification

Primary: 16A38, 16A38

Secondary: 16A42

Milestones

Received: 9 August 1978

Published: 1 July 1979