Projective Modules and Efficient Generation of Ideals Over Laurent Polynomial Rings

Abstract

Let A be commutative Noetherian ring of dimension d. In this paper we show that every finitely generated projective \(A[X_1, X_2, \ldots , X_r]\)-module of constant rank n is generated by \(n+d\) elements. We also extend some results over the Laurent polynomial ring \(A[X,X^{-1}]\), which are true for polynomial rings.