Difference between revisions of "Stably free module"
From Encyclopedia of Mathematics
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Latest revision as of 15:03, 19 November 2023
2020 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=54547
Stably free module. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Stably_free_module&oldid=54547