false for a not a root of this equation, that is, for a outside The fundamental theorem of additive polynomials Let P(x) be a polynomial with coefficients in k, and be the set of its roots. Assuming that the roots of P(x) are distinct (that is, P(x) is separable), then P(x) is additive if and only if the set forms a group with the field addition. See also Drinfeld module Additive map References David Goss, Basic Structures of Function Field Arithmetic, 1996, Springer, Berlin. . External links Algebraic number theory Modular arithmetic Polynomials