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 lumberers rarely trouble themselves to put out their fires, such is the dampness of the primitive forest; and this is one cause, no doubt, of the frequent fires in Maine, of which we hear so much on smoky days in Massachusetts.”
    —Henry David Thoreau (1817–1862)

    “We have a great deal more kindness than is ever spoken. Maugre all the selfishness that chills like east winds the world, the whole human family is bathed with an element of love like a fine ether.”
    —Ralph Waldo Emerson (1803–1882)