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 M* = Hom(M,R) 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.
YouTube Encyclopedic
-
1/3Views:89 51658 0401 353
-
Extended Euclidean Algorithm and Inverse Modulo Tutorial
-
How To Find The Inverse of a Number ( mod n ) - Inverses of Modular Arithmetic - Example
-
Mod-01 Lec-07 Invertible matrices, Homogeneous Equations Non-homogeneous Equations
Transcription
See also
References
- Eisenbud, David, Commutative Algebra with a View Toward Algebraic Geometry, Springer, ISBN 978-0-387-94269-8