Factoring biquadratic maps on modules

Abstract

This paper continues a line of investigation into the connection between the fimctional equation (*) F(x, y) 2 = F(x, x) F(y, y) and the existence of a factorization (t) F(x, y) = ocf(x)f(y). We prove first a fundamental lemma concerning Solutions of (*) which take values in a unique factorization domain R. With this, we derive an improved Version of a result in [2] about biadditive maps. Then we examine Symmetrie biquadratic Solutions of (*) for F: M x M -> R, where M is a free Λ'-module and R' is a subring of R. Our main results show that such an Fadmits a factorization (|), where/is quadratic.