primitive element

Meanings

1. An element that generates a simple extension.
2. An element that generates the multiplicative group of a given Galois field (finite field).
3. 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.
4. An element that is not a positive integer multiple of another element of the lattice.
5. 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).
6. An element of a free generating set of a given free group.

Translations