Bounds on the minimal number of generators of the dual module.

Let (A , m A) be a Cohen–Macaulay local ring. Let M be a finitely generated A -module and let M ∗ denote the A -dual of M. Furthermore, if M ∗ is a maximal Cohen–Macaulay A -module, then we prove that μ A (M ∗) ≤ μ A (M) e (A) , where μ A (M) is the cardinality of a minimal generating set of M as an A -module and e (A) is the multiplicity of the local ring A. Furthermore, if M is a reflexive A -module then μ A (M) e (A) ≤ μ A (M ∗). As an application, we study the bound on the minimal number of generators of specific modules over two-dimensional normal local rings. We also mention some relevant examples. [ABSTRACT FROM AUTHOR]