primitive element (English, noun)
expansion: primitive element (plural primitive elements)
Senses:
topics: algebra
mathematics
sciences
qualifier: field theory
glosses: An element that generates a simple extension.
topics: algebra
mathematics
sciences
qualifier: field theory
glosses: An element that generates the multiplicative group of a given Galois field (finite field).
raw_tags: of a finite field
topics: mathematics
number-theory
sciences
glosses: 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.
topics: algebra
mathematics
sciences
qualifier: lattice theory
glosses: An element that is not a positive integer multiple of another element of the lattice.
raw_tags: of a lattice
topics: algebra
mathematics
sciences
glosses: 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).
raw_tags: of a coalgebra over an element g
topics: group-theory
mathematics
sciences
glosses: An element of a free generating set of a given free group.
raw_tags: of a free group
Forms:
form: primitive elements
tags: plural