A Note on Characters of Algebraic Groups
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..
Broughton, S.A. (1983). A note on characters of algebraic groups. In R.R. Goldberg, et al. (Eds.), Proceedings of the American Mathematical Society, 89(1), 39-40.