Commutative algebra Polynomial rings and invariants Concept
Polynomial ring
Summary
The polynomial ring over a ring is the ring of the polynomials in one variable with coefficients in . The definition of the polynomial ring gives the construction.
Where this leads
67 pages build on this one.
- Artin approximation theorem
- Regular local rings are UFDs
- Algebraic set
- Linear recurrence with polynomial coefficients
- Hochster–Roberts theorem
- Gröbner basis
- Ideal of an algebraic set
- Rees algebra
- Serre's problem on projective modules
- Quillen–Suslin theorem
- Noether normalization lemma
- Continuous functional calculus
- Generic matrix algebra
- Jacobian conjecture
- Regular chain
- Witt vectors
- Formally smooth map
- Hilbert's Nullstellensatz
- Coordinate ring
- De Rham cohomology of varieties
- Dixmier conjecture
- Positivstellensatz
- abc conjecture
- Jacobian criterion
- Castelnuovo–Mumford regularity
- Multivariate division algorithm
- Free algebra
- Monomial order
- Bergman's gap theorem
- Determinantal ideal
- Hilbert's fourteenth problem
- Crystalline cohomology
- Holonomic function
- Algebraic statistics
- Stanley–Reisner ring
- Commutative Gelfand–Naimark theorem
- Universally catenary ring
- Spectral mapping theorem for polynomials
- Finite type algebra
- Pincherle derivative
- Hilbert's syzygy theorem
- Bernstein–Sato polynomial
- Kähler differentials
- Ring of invariants
- Chebyshev polynomials of the second kind
- Noncommutative geometry
- Hölder's theorem
- Dimension of a polynomial ring
- Gelfand's spectral radius formula
- Elimination theory
- Regular local rings are domains
- Henselian ring
- Integral element
- AKS primality test
- Toric ideal
- Finitely presented algebra
- Affine variety
- Buchberger's algorithm
- Nagata's example of a Noetherian ring of infinite dimension
- Integer factorization
- Gelfand–Kirillov dimension
- Plane curve
- Monomial ideal
- Lagrange basis polynomials
- Smooth morphism of rings
- Mason–Stothers theorem
- Weak Nullstellensatz
Further reading
- Web https://en.wikipedia.org/wiki/Polynomial_ring, lead section
About this page
| Tag | 0SDC934R52 |
|---|---|
| URI | m2://0SDC934R52 |
| Kind | concept |
| Writing | W1 stated |
| MSC | 13F20 |
| 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)
- edge specializes both: the more general notions and the special cases (0 of 1)
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What links here
Definitions
Used by
- Artin approximation theorem
- Algebraic set
- Linear recurrence with polynomial coefficients
- Hochster–Roberts theorem
- Gröbner basis
- Ideal of an algebraic set
- Rees algebra
- Serre's problem on projective modules
- Quillen–Suslin theorem
- Noether normalization lemma
- Generic matrix algebra
- Jacobian conjecture
- Regular chain
- Witt vectors
- Formally smooth map
- Hilbert's Nullstellensatz
- Coordinate ring
- Jacobian criterion
- Castelnuovo–Mumford regularity
- Multivariate division algorithm
- Free algebra
- Monomial order
- Bergman's gap theorem
- Determinantal ideal
- Hilbert's fourteenth problem
- Holonomic function
- Algebraic statistics
- Stanley–Reisner ring
- Universally catenary ring
- Spectral mapping theorem for polynomials
- Finite type algebra
- Pincherle derivative
- Hilbert's syzygy theorem
- Bernstein–Sato polynomial
- Kähler differentials
- Ring of invariants
- Chebyshev polynomials of the second kind
- Hölder's theorem
- Dimension of a polynomial ring
- Elimination theory
- Regular local rings are domains
- Henselian ring
- Integral element
- AKS primality test
- Toric ideal
- Finitely presented algebra
- Buchberger's algorithm
- Nagata's example of a Noetherian ring of infinite dimension
- Gelfand–Kirillov dimension
- Plane curve
- Monomial ideal
- Lagrange basis polynomials
- Smooth morphism of rings
- Mason–Stothers theorem
- Weak Nullstellensatz