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 <math> M_P\cong R_P </math> for all primes P of R.

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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 <math> M_P\cong R_P </math> 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. <math>M\otimes _R M^*\cong R</math>. The theory of invertible modules is closely related to the theory of codimension one varieties including the theory of divisors.
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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 <math> M_P\cong R_P </math> for all primes P of R.
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  • Invertible module
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