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 for all primes P of R. Now, if M is an invertible R-module, then its dual .

The theory of invertible modules is closely related to the theory of codimension one varieties including the theory of divisorss.

See also

• Picard group

References

• Eisenbud, David, Commutative Algebra with a View Toward Algebraic Geometry, Springer,