Commutative algebra Homological methods Concept
Projective resolution
Summary
A projective resolution of a module is an exact sequence of projective modules that ends in . It replaces by a complex of simple pieces that has the same homological information. Every module has a projective resolution, and the derived functors such as Ext and Tor are computed from it.
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About this page
| Tag | HK2AA1YSQ2 |
|---|---|
| URI | m2://HK2AA1YSQ2 |
| Kind | concept |
| Writing | W0 stub |
| MSC | 13D02, 18G10 |
| Changed | 2 November 2026 |
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Used by
- Betti numbers of a module
- Projective dimension
- Hilbert–Burch theorem
- Cohomological dimension of a group
- Ext functor
- Castelnuovo–Mumford regularity
- Group homology
- Tor functor
- Hilbert's syzygy theorem