Associative rings and algebras Modules and ideals Concept
Free module
Summary
A free module is a module that has a basis, that is, a linearly independent generating set.
Where this leads
20 pages build on this one.
- Betti numbers of a module
- Koszul complex
- Serre's problem on projective modules
- Quillen–Suslin theorem
- Nichols–Zoeller theorem
- Bar resolution
- Finitely generated projective modules over local rings are free
- Hecke algebra
- Kaplansky's theorem on projective modules
- Projective module
- Bass's theorem P
- Ore extension
- Eilenberg swindle
- Hilbert's syzygy theorem
- Projective resolution
- Tensor product of modules
- Structure theorem for finitely generated modules over a principal ideal domain
- Invariant basis number
- Azumaya algebra
- Finitely presented module
Further reading
- Web https://en.wikipedia.org/wiki/Free_module, Definition
About this page
| Tag | 0DZ9DKAKZR |
|---|---|
| URI | m2://0DZ9DKAKZR |
| Kind | concept |
| Writing | W1 stated |
| MSC | 16D40, 13C10 |
| Specializes | Module over a ring |
| Same as |
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What this page needs for W2
- edge instance_of in: at least two examples (0 of 2)
- edge not_instance_of in: at least one non-example (0 of 1)
The writing levels say how complete the text of a page is. They do not measure its truth.
What links here
Definitions
Used by
- Betti numbers of a module
- Koszul complex
- Serre's problem on projective modules
- Quillen–Suslin theorem
- Nichols–Zoeller theorem
- Bar resolution
- Finitely generated projective modules over local rings are free
- Hecke algebra
- Projective module
- Ore extension
- Eilenberg swindle
- Hilbert's syzygy theorem
- Projective resolution
- Tensor product of modules
- Structure theorem for finitely generated modules over a principal ideal domain
- Invariant basis number
- Finitely presented module