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:
“There is always a degree of ridicule that attends a disappointment, though often very unjustly, if the expectation was reasonably grounded; however, it is certainly most prudent not to communicate, prematurely, one’s hopes or one’s fears.”
—Philip Dormer Stanhope, 4th Earl Chesterfield (1694–1773)
“Unintelligent persons are like weeds that thrive in good ground; they love to be amused in proportion to the degree in which they weary themselves.”
—Honoré De Balzac (1799–1850)
“I don’t like comparisons with football. Baseball is an entirely different game. You can watch a tight, well-played football game, but it isn’t exciting if half the stadium is empty. The violence on the field must bounce off a lot of people. But you can go to a ball park on a quiet Tuesday afternoon with only a few thousand people in the place and thoroughly enjoy a one-sided game. Baseball has an aesthetic, intellectual appeal found in no other team sport.”
—Bowie Kuhn (b. 1926)
“The desert is a natural extension of the inner silence of the body. If humanity’s language, technology, and buildings are an extension of its constructive faculties, the desert alone is an extension of its capacity for absence, the ideal schema of humanity’s disappearance.”
—Jean Baudrillard (b. 1929)