Invertible module
In mathematics, particularly commutative algebra, an invertible module is intuitively a module that has an inverse with respect to the tensor product. Invertible modules form the foundation for the definition of invertible sheaves in algebraic geometry.
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, for all primes P of R. Now, if M is an invertible R-module, then its dual is its inverse with respect to the tensor product, i.e..
The theory of invertible modules is closely related to the theory of codimension one varieties including the theory of divisors.
