Difference between revisions of "Stably free module"
From Encyclopedia of Mathematics
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A [[module]] which is close to being [[free module|free]]. | A [[module]] which is close to being [[free module|free]]. | ||
Revision as of 13:30, 12 December 2013
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=31030
Stably free module. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Stably_free_module&oldid=31030