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Stably free module

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2010 Mathematics Subject Classification: Primary: 16D [MSN][ZBL]

A module which is close to being free.

A module $M$ over a ring $R$ is stably free if there exist free modules $F$ and $G$ over $R$ such that $$ M \oplus F = G \ . $$

A projective module is stably free if and only if it possesses a finite free resolution.

References

  • Serge Lang, Algebra 3rd ed (Addison-Wesley, 1993) ISBN 0-201-55540-9 p.840
How to Cite This Entry:
Stably free module. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Stably_free_module&oldid=35018