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:
“A certain degree of miserey [sic] seems inseparable from a high degree of populousness.”
—James Madison (17511836)
“Wonderful Force of Public Opinion! We must act and walk in all points as it prescribes; follow the traffic it bids us, realise the sum of money, the degree of influence it expects of us, or we shall be lightly esteemed; certain mouthfuls of articulate wind will be blown at us, and this what mortal courage can front?”
—Thomas Carlyle (17951881)
“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)
“Predatory capitalism created a complex industrial system and an advanced technology; it permitted a considerable extension of democratic practice and fostered certain liberal values, but within limits that are now being pressed and must be overcome. It is not a fit system for the mid- twentieth century.”
—Noam Chomsky (b. 1928)