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:

    “It would be some advantage to live a primitive and frontier life, though in the midst of an outward civilization, if only to learn what are the gross necessaries of life and what methods have been taken to obtain them.”
    —Henry David Thoreau (1817–1862)

    “What was any art but an effort to make a sheath, a mould in which to imprison for a moment the shining, elusive element which is life itself—life hurrying past us and running away, too strong to stop, too sweet to lose?”
    —Willa Cather (1873–1947)