Degree (mathematics) - Degree of A Field Extension

Degree of A Field Extension

Given a field extension K/F, the field K can be considered as a vector space over the field F. The dimension of this vector space is the degree of the extension and is denoted by .

Read more about this topic:  Degree (mathematics)

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

    [F]or as Socrates says that a wise man is a citizen of the world, so I thought that a wise woman was equally at liberty to range through every station or degree of men, to fix her choice wherever she pleased.
    Sarah Fielding (1710–1768)

    In the mass of mankind, I fear, there is too great a majority of fools and knaves; who, singly from their number, must to a certain degree be respected, though they are by no means respectable.
    Philip Dormer Stanhope, 4th Earl Chesterfield (1694–1773)

    I see a girl dragged by the wrists
    Across a dazzling field of snow,
    And there is nothing in me that resists.
    Once it would not be so....
    Philip Larkin (1922–1986)

    We are now a nation of people in daily contact with strangers. Thanks to mass transportation, school administrators and teachers often live many miles from the neighborhood schoolhouse. They are no longer in daily informal contact with parents, ministers, and other institution leaders . . . [and are] no longer a natural extension of parental authority.
    James P. Comer (20th century)