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:
“The world is burdened with young fogies. Old men with ossified minds are easily dealt with. But men who look young, act young and everlastingly harp on the fact that they are young, but who nevertheless think and act with a degree of caution that would be excessive in their grandfathers, are the curse of the world. Their very conservatism is secondhand, and they don’t know what they are conserving.”
—Robertson Davies (b. 1913)
“There can be a true grandeur in any degree of submissiveness, because it springs from loyalty to the laws and to an oath, and not from baseness of soul.”
—Simone Weil (1909–1943)
“Yet, hermit and stoic as he was, he was really fond of sympathy, and threw himself heartily and childlike into the company of young people whom he loved, and whom he delighted to entertain, as he only could, with the varied and endless anecdotes of his experiences by field and river: and he was always ready to lead a huckleberry-party or a search for chestnuts and grapes.”
—Ralph Waldo Emerson (1803–1882)
“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)