Free resolution: Difference between revisions
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===Symbol-free 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 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. | ||
==Related notions== | ==Related notions== | ||
Revision as of 03:12, 21 August 2007
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.