The ring of polynomials with coefficients in a field k. k[x] is a Euclidean domain; irreducible polynomials play the role of primes.
Polynomial ring k[x]
Related concepts
- Ring (R, +, ·)
- Field
- Galois theory
- Fundamental theorem of algebra
- λ (Conway's constant)
- Schur function
- Symmetric function
- UFD / PID / Euclidean domain hierarchy
- Lagrange interpolation
- Affine variety
- Hilbert basis theorem
- Gröbner basis
- Hilbert's Nullstellensatz
- Chebyshev polynomials T_n: orthogonal basis + minimax optimality
- Padé approximant [m/n]: rational P_m/Q_n matching Taylor to order m+n
- T_2(x) = 2x² − 1: alternation (−1,0,1)→(1,−1,1); roots at ±√2/2