K-theory K0 and projective modules Concept
Stably free module
Summary
A module is stably free if it becomes free after adding a free module of finite rank. Every free module of finite rank is stably free, but the converse fails in general. A finitely generated projective module is stably free exactly when its class in reduced is zero. So cannot tell a stably free module from a free one. The question of when stably free modules are free is a central theme of the theory of projective modules.
Further reading
About this page
| Tag | YMXJ4JTQPF |
|---|---|
| URI | m2://YMXJ4JTQPF |
| Kind | concept |
| Writing | W0 stub |
| MSC | 19A13, 13C10 |
| Specializes | Finitely generated projective module |
| Same as | |
| Changed | 3 November 2026 |
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