# Invertible module

Formally, a finitely generated module M over a ring R is said to be invertible if it is locally a free module of rank 1. In other words $M_P\cong R_P$ for all primes P of R. Now, if M is an invertible R-module, then its dual M* = Hom(M,R) is its inverse with respect to the tensor product, i.e. $M\otimes _R M^*\cong R$.