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| | In [[mathematics]], a '''stably free module''' is a [[module (mathematics)|module]] which is close to being [[free module|free]]. |
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| | ==Definition== |
| | A finitely generated module ''M'' over a ring ''R'' is ''stably free'' if there exist free finitely generated modules ''F'' and ''G'' over ''R'' such that |
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| | :<math> M \oplus F = G . \, </math> |
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| | ==Properties== |
| | * A projective module is stably free if and only if it possesses a finite [[free resolution]] (Theorem XXI.2.1 of Lang's '''Algebra'''). |
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| | == See also == |
| | * [[Free object]] |
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| | ==References== |
| | * Page 840 of {{Lang Algebra|edition=3}} |
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| | [[Category:Module theory]] |
| | [[Category:Free algebraic structures]] |
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| | |
| | {{Abstract-algebra-stub}} |
Revision as of 18:11, 31 December 2013
In mathematics, a stably free module is a module which is close to being free.
Definition
A finitely generated module M over a ring R is stably free if there exist free finitely generated modules F and G over R such that
Properties
- A projective module is stably free if and only if it possesses a finite free resolution (Theorem XXI.2.1 of Lang's Algebra).
See also
References
Template:Abstract-algebra-stub