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:
“I began to realize that it was bigotry of the worst kind to say that it’s better to be dead than to be born retarded or blind or without a limb. It’s a value judgment you’re making about someone’s life, based on their degree of perfection.”
—Juli Loesch (b. c. 1953)
“Essential truth, the truth of the intellectualists, the truth with no one thinking it, is like the coat that fits tho no one has ever tried it on, like the music that no ear has listened to. It is less real, not more real, than the verified article; and to attribute a superior degree of glory to it seems little more than a piece of perverse abstraction-worship.”
—William James (1842–1910)
“The frequent failure of men to cultivate their capacity for listening has a profound impact on their capacity for parenting, for it is mothers more than fathers who are most likely to still their own voices so they may hear and draw out the voices of their children.”
—Mary Field Belenky (20th century)
“The motive of science was the extension of man, on all sides, into Nature, till his hands should touch the stars, his eyes see through the earth, his ears understand the language of beast and bird, and the sense of the wind; and, through his sympathy, heaven and earth should talk with him. But that is not our science.”
—Ralph Waldo Emerson (1803–1882)