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 think of a hero as someone who understands the degree of responsibility that comes with his freedom.”
—Bob Dylan [Robert Allen Zimmerman] (b. 1941)
“In the mass of mankind, I fear, there is too great a majority of fools and knaves; who, singly from their number, must to a certain degree be respected, though they are by no means respectable.”
—Philip Dormer Stanhope, 4th Earl Chesterfield (1694–1773)
“I learn immediately from any speaker how much he has already lived, through the poverty or the splendor of his speech. Life lies behind us as the quarry from whence we get tiles and copestones for the masonry of today. This is the way to learn grammar. Colleges and books only copy the language which the field and the work-yard made.”
—Ralph Waldo Emerson (1803–1882)
“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)