Commutative algebra Modules Concept
Finitely generated module
Summary
A finitely generated module is a module in which every element is a linear combination of a fixed finite set of elements.
Where this leads
36 pages build on this one.
- Betti numbers of a module
- Nakayama's lemma
- Regular local rings are UFDs
- Krull intersection theorem
- Hilbert–Samuel function
- Artin–Rees lemma
- Artin–Tate lemma
- Hilbert polynomial
- Finite morphism
- Serre's problem on projective modules
- Quillen–Suslin theorem
- Finitely generated projective modules over local rings are free
- Finite morphism of rings
- Determinant trick
- Direct summand conjecture
- Canonical module
- Coherent sheaf
- Hilbert–Serre theorem
- Castelnuovo–Mumford regularity
- Progenerator
- Depth
- Completion is flat
- Order (ring theory)
- Picard group of a ring
- Hilbert's syzygy theorem
- Jordan–Zassenhaus theorem
- Cayley–Hamilton theorem for modules
- Auslander–Buchsbaum formula
- Structure theorem for finitely generated modules over a principal ideal domain
- Regular local rings are domains
- Grothendieck's local duality
- Morita duality
- Nagata ring
- Hilbert scheme
- Finitely presented module
- Transitivity of integrality
Further reading
About this page
| Tag | 05QY1VEBYD |
|---|---|
| URI | m2://05QY1VEBYD |
| Kind | concept |
| Writing | W1 stated |
| MSC | 13E15, 16D10 |
| 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
- Nakayama's lemma
- Krull intersection theorem
- Hilbert–Samuel function
- Artin–Rees lemma
- Artin–Tate lemma
- Hilbert polynomial
- Finite morphism
- Serre's problem on projective modules
- Quillen–Suslin theorem
- Finitely generated projective modules over local rings are free
- Finite morphism of rings
- Determinant trick
- Direct summand conjecture
- Canonical module
- Coherent sheaf
- Hilbert–Serre theorem
- Castelnuovo–Mumford regularity
- Progenerator
- Depth
- Completion is flat
- Order (ring theory)
- Picard group of a ring
- Hilbert's syzygy theorem
- Jordan–Zassenhaus theorem
- Cayley–Hamilton theorem for modules
- Auslander–Buchsbaum formula
- Structure theorem for finitely generated modules over a principal ideal domain
- Grothendieck's local duality
- Morita duality
- Nagata ring
- Finitely presented module
- Transitivity of integrality
Results about this
- Nakayama's lemma
- Determinant trick
- Cayley–Hamilton theorem for modules
- Structure theorem for finitely generated modules over a principal ideal domain