polynomial basis

(algebra, ring theory) A basis of a polynomial ring (said ring being viewed either as a vector space over the field of coefficients or as a free module over the ring of coefficients).

(algebra, field theory, cryptography, of a finite field) Specifically, a basis, of the form {1, α, ..., αⁿ⁻¹}, of a finite extension F_(qⁿ) of a Galois field F_q, where α is a primitive element of F_(qⁿ) (i.e., a root of a degree-n primitive polynomial over F_q).