In mathematics, the term primitive element can mean:
- Primitive root 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 algebra, an element X on which the comultiplication Δ has the value Δ(X) = X⊗1 + 1⊗X
- in a free group, an element of a free generating set
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