Free resolution

Definition

Symbol-free definition

A free resolution of a module over a commutative unital ring is an exact sequence of modules (possibly infinite in length) terminating at 0, with the second last member being the given module, and where all preceding members are free modules.

Metaproperties

Given a fixed module $M$, free resolutions of $M$ are unique up to chain homotopy.

Related notions

• Injective resolution
• Koszul complex of a module
• Minimal resolution
• Projective resolution