Projective resolution: Difference between revisions
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===Symbol-free definition=== | ===Symbol-free definition=== | ||
A '''projective resolution''' of a module is an [[exact sequence of modules]] (possibly infinite in length) terminating at the given module, and such that all preceding members of the exact sequence are [[projective module]]s. | A '''projective 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 such that all preceding members of the exact sequence are [[projective module]]s. | ||
==Related notions== | ==Related notions== | ||
Revision as of 03:12, 21 August 2007
Definition
Symbol-free definition
A projective 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 such that all preceding members of the exact sequence are projective modules.