In [[mathematics]], a '''stably free module''' is a [[module (mathematics)|module]] which is close to being [[free module|free]].
==Definition== A module ''M'' over a ring ''R'' is ''stably free'' if there exists a free [[finitely generated module]] ''F'' over ''R'' such that <math> M \oplus F</math> is a free module.
==Properties== * A [[projective module]] is stably free if and only if it possesses a finite [[free resolution]].<ref>{{Lang Algebra|edition=3}}</ref> * An [[infinitely generated module]] is stably free if and only if it is free.<ref>{{cite book|author=Lam, T. Y. |author-link=Tsit Yuen Lam |title=Serre's Conjecture|year=1978|url={{Google books|plainurl=y|id=f-t6CwAAQBAJ|page=23|text=If P is stably free, but not finitely generated, then P is actually free.}}|page=23}}</ref>
== See also == * [[Free object]] * [[Eilenberg–Mazur swindle]] * [[Hermite ring]]
== References == {{Reflist}}
[[Category:Module theory]] [[Category:Free algebraic structures]]
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