Primitive element
Encyclopedia
In mathematics, the term primitive element can mean:
- Primitive root modulo nPrimitive root modulo nIn modular arithmetic, a branch of number theory, a primitive root modulo n is any number g with the property that any number coprime to n is congruent to a power of g modulo n. In other words, g is a generator of the multiplicative group of integers modulo n...
, in number theory - Primitive element (field theory), an element that generates a given field extension
- Primitive element (finite field), an element that generates the multiplicative group of a finite field
- in a Hopf algebraHopf algebraIn mathematics, a Hopf algebra, named after Heinz Hopf, is a structure that is simultaneously an algebra and a coalgebra, with these structures' compatibility making it a bialgebra, and that moreover is equipped with an antiautomorphism satisfying a certain property.Hopf algebras occur naturally...
, an element X on which the comultiplication Δ has the value Δ(X) = X⊗1 + 1⊗X - in a free groupFree groupIn mathematics, a group G is called free if there is a subset S of G such that any element of G can be written in one and only one way as a product of finitely many elements of S and their inverses...
, an element of a free generating set