invertible ideals are projective
If is a ring and is a homomorphism of -modules, then a right inverse of is a homomorphism such that is the identity map on . For a right inverse to exist, it is clear that must be an epimorphism. If a right inverse exists for every such epimorphism and all modules , then is said to be a projective module.
Let be an integral domain. Then a fractional ideal over is invertible if and only if it is projective as an -module.
In particular, every fractional ideal over a Dedekind domain is invertible, and is therefore projective.
|Title||invertible ideals are projective|
|Date of creation||2013-03-22 18:35:47|
|Last modified on||2013-03-22 18:35:47|
|Last modified by||gel (22282)|