the generalized principal ideal theorem is one of the cornerstones of dimension theory for noetherian rings. for an r-module m, we identify certain submodules of m that play a role analogous to that of prime ideals in the ring r. using this definition, we extend the generalized principal ideal theorem to modules.

The Bieberbach conjecture about the coefficients of univalent functions of the unit disk was formulated by Ludwig Bieberbach in 1916 [4]. The conjecture states that the coefficients of univalent functions are majorized by those of the Koebe function which maps the unit disk onto a radially slit plane. The Bieberbach conjecture was quite a difficult problem, and it was surprisingly proved by Lou...