Definitions from Wiktionary (primitive element)

▸ noun:  (algebra, field theory) An element that generates a simple extension.
▸ noun:  (algebra, field theory, of a finite field) An element that generates the multiplicative group of a given Galois field (finite field).
▸ noun:  (number theory) 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.
▸ noun:  (algebra, lattice theory, of a lattice) An element that is not a positive integer multiple of another element of the lattice.
▸ noun:  (algebra, of a coalgebra over an element g) 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).
▸ noun:  (group theory, of a free group) An element of a free generating set of a given free group.





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