Free resolution: Difference between revisions
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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 module]]s. | 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 module]]s. | ||
==Metaproperties== | |||
Given a fixed module <math>M</math>, free resolutions of <math>M</math> are unique up to [[chain homotopy]]. | |||
==Related notions== | ==Related notions== | ||
* [[Injective resolution]] | * [[Injective resolution]] | ||
* [[Koszul complex of a module]] | * [[Koszul complex of a module]] | ||
* [[Minimal resolution]] | |||
* [[Projective resolution]] | |||
Latest revision as of 18:46, 3 January 2009
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 , free resolutions of are unique up to chain homotopy.
