ABSTRACT
From F(a , . . . , o m(a)) = 0, we deduce that o(F){p{a) , . . . , o m+x(a)) = 0, so that the minimal polynomial of am+x{a) over E(a , . . . , a m(a)) divides o(F)(a(a) , . . . , o m(a), Y), and therefore has degree bounded above by the degree of F(a , . . . ,crm -l(a), F). It follows that IG {a/E), as a cr-ideal, is finitely generated, since from some point on, the degree of the minimal polynomial of on(a) over E(a , . . . , on~x{a)) must stabilize.
