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:
“In all pointed sentences, some degree of accuracy must be sacrificed to conciseness.”
—Samuel Johnson (17091784)
“Maybe men are separated from each other only by the degree of their misery.”
—Francis Picabia (18781953)
“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)
“After all the field of battle possesses many advantages over the drawing-room. There at least is no room for pretension or excessive ceremony, no shaking of hands or rubbing of noses, which make one doubt your sincerity, but hearty as well as hard hand-play. It at least exhibits one of the faces of humanity, the former only a mask.”
—Henry David Thoreau (18171862)
“Slavery is founded in the selfishness of mans natureopposition to it, is [in?] his love of justice.... Repeal the Missouri compromiserepeal all compromisesrepeal the declaration of independencerepeal all past history, you still can not repeal human nature. It still will be the abundance of mans heart, that slavery extension is wrong; and out of the abundance of his heart, his mouth will continue to speak.”
—Abraham Lincoln (18091865)