Degree of A Field Extension

In mathematics, more specifically field theory, the degree of a field extension is a rough measure of the "size" of the extension. The concept plays an important role in many parts of mathematics, including algebra and number theory — indeed in any area where fields appear prominently.

Read more about Degree Of A Field Extension:  Definition and Notation, The Multiplicativity Formula For Degrees, Examples, Generalization

Famous quotes containing the words degree of, degree, field and/or extension:

    I never saw, heard, nor read, that the clergy were beloved in any nation where Christianity was the religion of the country. Nothing can render them popular, but some degree of persecution.
    Jonathan Swift (1667–1745)

    A new degree of intellectual power seems cheap at any price.
    Ralph Waldo Emerson (1803–1882)

    The birds their quire apply; airs, vernal airs,
    Breathing the smell of field and grove, attune
    The trembling leaves, while universal Pan,
    Knit with the Graces and the Hours in dance,
    Led on th’ eternal Spring.
    John Milton (1608–1674)

    The medium is the message. This is merely to say that the personal and social consequences of any medium—that is, of any extension of ourselves—result from the new scale that is introduced into our affairs by each extension of ourselves, or by any new technology.
    Marshall McLuhan (1911–1980)