Dual module
In mathematics, the dual module of a left module M over a ring R is the set of module homomorphisms from M to R with the pointwise right module structure. The dual module is typically denoted M∗ or.
If the base ring R is a field, then a dual module is a dual vector space.
Every module has a canonical homomorphism to the dual of its dual. A reflexive module is one for which the canonical homomorphism is an isomorphism. A torsionless module is one for which the canonical homomorphism is injective.
Example: If is a finite commutative group scheme represented by a Hopf algebra A over a commutative ring k, then the Cartier dual is the Spec of the dual k-module of A.
