Let R be a commutative ring. Let A be a free R-algebra of finite rank and M be a free bilinear A-module of finite rank. In this work, we establish an interesting tower formula of discriminant of  More precisely, we prove that the discriminant of the bilinear module M over R is the product of the norm of discriminant of bilinear module M over A and some power of the classical discriminant of the R‑algebra A. As an application we compute the discriminant of the algebra associated to a B-J polynomial, and the discriminant of some graded fields.

discriminant, bilinear form, transitivity.