Projective dimension of a module: Difference between revisions
No edit summary |
|||
| Line 8: | Line 8: | ||
* [[Injective dimension of a module]] | * [[Injective dimension of a module]] | ||
* [[ | * [[Global dimension of a ring]] | ||
Revision as of 03:21, 21 August 2007
Definition
Symbol-free definition
The projective dimension of a module over a commutative unital ring is defined as the minimum of the lengths of finite projective resolutions of the module (here, the length is the number of members apart from the module itself and zero). If there is no projective resolution of finite length, the projective dimension is taken as .
