Invertible module
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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
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.
See also
References
- ISBN 978-0-387-94269-8