Let be a commutative ring, and let be a commutative -algebra. A universal derivation of over is defined to be an -module together with an -linear derivation , such that the following universal property holds: for every -module and every -linear derivation there exists a unique -linear map such that .
The universal property can be illustrated by a commutative diagram:
An -module with this property can be constructed explicitly, so always exists. It is generated as an -module by the set , with the relations
for all and .
The universal property implies that is unique up to a unique isomorphism. The -module is often called the module of Kähler differentials.
|Date of creation||2013-03-22 15:27:57|
|Last modified on||2013-03-22 15:27:57|
|Last modified by||pbruin (1001)|