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 a, degree of, degree, field and/or extension:
“But in every constitution some large degree of animal vigor is necessary as material foundation for the higher qualities of the art.”
—Ralph Waldo Emerson (18031882)
“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 (19091943)
“To the degree that respect for professors ... has risen in our society, respect for writers has fallen. Today the professorial intellect has achieved its highest public standing since the world began, while writers have come to be called men of letters, by which is meant people who are prevented by some obscure infirmity from becoming competent journalists.”
—Robert Musil (18801942)
“An enormously vast field lies between God exists and there is no God. The truly wise man traverses it with great difficulty. A Russian knows one or the other of these two extremes, but is not interested in the middle ground. He usually knows nothing, or very little.”
—Anton Pavlovich Chekhov (18601904)
“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)