primitive element

Definitions

1. 1

   An element that generates a simple extension.

2. 2

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

   • Furthermore, if the irreducible polynomial has a primitive element α (where α=1) that is a root, then the polynomial is termed a primitive polynomial and corresponds to the polynomial for a maximal length feedback shift register.
   • Here, necessarily, c must be a primitive element of 𝔽_𝕢, since this is the norm of a root of the polynomial.
3. 3

   Given a modulus n, a number g such that every number coprime to n is congruent (modulo n)…

   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.

   • Let A be a prime number for which 2 is a primitive element. Then 2#123;A-1#125;-1 is divisible by A.
4. ›+ 3 more definitionsshow fewer

   1. 4

      An element that is not a positive integer multiple of another element of the lattice.

   2. 5

      An element x ∈ C such that μ(x) = x ⊗ g + g ⊗ x, where μ is the comultiplication and g is…

      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).

   3. 6

      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.

The neighborhood

• synonymprimitive root
• neighborprimitive polynomial
• neighborprimitive root