Projective dimension of a module

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 $\infty$.

Related notions

• Injective dimension of a module
• Global dimension of a ring