Primitive Element

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

Famous quotes containing the words primitive and/or element:

    “The most primitive places left with us are the swamps, where the spruce still grows shaggy with usnea.”
    —Henry David Thoreau (1817–1862)

    “Cranks live by theory, not by pure desire. They want votes, peace, nuts, liberty, and spinning-looms not because they love these things, as a child loves jam, but because they think they ought to have them. That is one element which makes the crank.”
    —Rose Macaulay (1881–1958)