Polynomially linked additive functions—II.

We continue the study of additive functions fk:R→F(1≤k≤n)<inline-graphic></inline-graphic> linked by an equation of the form ∑k=1npk(x)fk(qk(x))=0<inline-graphic></inline-graphic>, where the pk<inline-graphic></inline-graphic> and qk<inline-graphic></inline-graphic> are polynomials, R is an integral domain of characteristic 0, and F is the fraction field of R. A method is presented for solving all such equations. We also consider the special case ∑k=1nxmkfk(xjk)=0<inline-graphic></inline-graphic> in which the pk<inline-graphic></inline-graphic> and qk<inline-graphic></inline-graphic> are monomials. In this case we show that if there is no duplication, i.e. if (mk,jk)≠(mp,jp)<inline-graphic></inline-graphic> for k≠p<inline-graphic></inline-graphic>, then each fk<inline-graphic></inline-graphic> is the sum of a linear function and a derivation of order at most n-1<inline-graphic></inline-graphic>. Furthermore, if this functional equation is not homogeneous then the maximal orders of the derivations are reduced in a specified way. [ABSTRACT FROM AUTHOR]