“Invertible module”的意思、由来-开放百科全书

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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 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 {{nowrap|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.

References

Eisenbud, David, Commutative Algebra with a View Toward Algebraic Geometry, Springer, {{ISBN|978-0-387-94269-8}}

2 : Mathematical structures|Algebra

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