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:
“I happen to feel that the degree of a person’s intelligence is directly reflected by the number of conflicting attitudes she can bring to bear on the same topic.”
—Lisa Alther (b. 1944)
“I would rather be exposed to the inconveniences attending too much liberty than those attending too small a degree of it.”
—Thomas Jefferson (1743–1826)
“When I tried to talk to my father about the kind of work I might do after college, he said, “You know, Charlotte, I’ve been giving a lot of thought to that, and it seems to me that the world really needs good, competent secretaries. Your English degree will help you.” He said this with perfect seriousness. I was an A student at Bryn Mawr ...”
—Charlotte Palmer (b. c. 1925)
“Better risk loss of truth than chance of error—that is your faith-vetoer’s exact position. He is actively playing his stake as much as the believer is; he is backing the field against the religious hypothesis, just as the believer is backing the religious hypothesis against the field.”
—William James (1842–1910)
“The medium is the message. This is merely to say that the personal and social consequences of any medium—that is, of any extension of ourselves—result from the new scale that is introduced into our affairs by each extension of ourselves, or by any new technology.”
—Marshall McLuhan (1911–1980)