A note on characters of algebraic groups

S. A. Broughton
1983 Proceedings of the American Mathematical Society  
It is proven that a nowhere-vanishing polynomial function on a connected algebraic group, over an algebraically closed field, is a multiple of a (one-dimensional) character.
doi:10.1090/s0002-9939-1983-0706506-x fatcat:642nqaoivnd3hebkn7ivf7rvrq