Difference between revisions of "Stably free module"
From Encyclopedia of Mathematics
(Start article: Stably free module) |
m (→References: isbn link) |
||
| (2 intermediate revisions by 2 users not shown) | |||
| Line 1: | Line 1: | ||
| + | {{TEX|done}}{{MSC|16D}} | ||
| + | |||
A [[module]] which is close to being [[free module|free]]. | A [[module]] which is close to being [[free module|free]]. | ||
| Line 9: | Line 11: | ||
==References== | ==References== | ||
| − | * Serge Lang, ''Algebra'' | + | * Serge Lang, ''Algebra'' 3<sup>rd</sup> ed (Addison-Wesley, 1993) {{ISBN|0-201-55540-9}} p.840 |
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=30516
Stably free module. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Stably_free_module&oldid=30516