In mathematics, more specifically in the area of modern algebra known as field theory, the primitive element theorem or Artin's theorem on primitive elements is a result characterizing the finite degree field extensions that possess a primitive element. More specifically, the primitive element theorem characterizes those finite degree extensions such that there exists with .
Read more about Primitive Element Theorem: Terminology, Existence Statement, Counterexamples, Constructive Results, Example
Famous quotes containing the words primitive, element and/or theorem:
“The mountainous region of the State of Maine stretches from near the White Mountains, northeasterly one hundred and sixty miles, to the head of the Aroostook River, and is about sixty miles wide. The wild or unsettled portion is far more extensive. So that some hours only of travel in this direction will carry the curious to the verge of a primitive forest, more interesting, perhaps, on all accounts, than they would reach by going a thousand miles westward.”
—Henry David Thoreau (1817–1862)
“To be radical, an empiricism must neither admit into its constructions any element that is not directly experienced, nor exclude from them any element that is directly experienced.”
—William James (1842–1910)
“To insure the adoration of a theorem for any length of time, faith is not enough, a police force is needed as well.”
—Albert Camus (1913–1960)