Dual module

In mathematics, the dual module of a left (resp. right) module M over a ring R is the set of module homomorphisms from M to R with the pointwise right (resp. left) module structure.^[1][2]

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 (called the double 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.

References

1. N. Bourbaki (1974). Algebra I. Springer. ISBN 9783540193739.
2. S. Lang (2002). Algebra. Springer. ISBN 978-0387953854.