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:

    It is a secret from nobody that the famous random event is most likely to arise from those parts of the world where the old adage “There is no alternative to victory” retains a high degree of plausibility.
    Hannah Arendt (1906–1975)

    His poor, crazy, deformed body was a mere Pandora’s box, containing all the physical ills that ever afflicted humanity. This, perhaps, whetted the edge of his satire, and may in some degree excuse it.
    Philip Dormer Stanhope, 4th Earl Chesterfield (1694–1773)

    Vigil strange I kept on the field one night;
    When you my son and my comrade dropt at my side that day,
    One look I but gave which your dear eyes return’d with a look I
    shall never forget,
    One touch of your hand to mine O boy, reach’d up as you lay on the ground,
    Walt Whitman (1819–1892)

    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)