Primitive Element Definition

(algebra PRIMITIVE ELEMENT that generates a simple extension .

(algebra PRIMITIVE ELEMENT that generates the multiplicative group of a given Galois field (finite field ).

Given a modulus n, a number g such that every number coprime to n is congruent (modulo n) to some power of g; equivalently, a generator of the multiplicative field of integers modulo n.

(algebra PRIMITIVE ELEMENT that is not a positive integer multiple of another element of the lattice .

(algebra PRIMITIVE ELEMENT x ∈ C such that μ(x) = x ⊗ g + g ⊗ x, where μ is the comultiplication and g is an element that maps to the multiplicative identity 1 of the base field under the counit (in particular, if C is a bialgebra , g = 1).