primitive element

noun6

1. •
   An element that generates the multiplicative group of a given Galois field (finite field).

   • Here, necessarily, c must be a primitive element of 𝔽_𝕢, since this is the norm of a root of the polynomial. — 2008
2. •
   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.
3. •
   An element that generates a simple extension.
4. •
   An element of a free generating set of a given free group.

   • In this paper we apply regression models and other pattern recognition techniques to the task of classifying primitive elements of a free group. — 2004
5. •
   An element that is not a positive integer multiple of another element of the lattice.
6. •
   An 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).