In mathematics, more specifically field theory, the degree of a field extension is a rough measure of the "size" of the extension. The concept plays an important role in many parts of mathematics, including algebra and number theory — indeed in any area where fields appear prominently.
Read more about Degree Of A Field Extension: Definition and Notation, The Multiplicativity Formula For Degrees, Examples, Generalization
Famous quotes containing the words degree of, degree, field and/or extension:
“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)
“I began to realize that it was bigotry of the worst kind to say that it’s better to be dead than to be born retarded or blind or without a limb. It’s a value judgment you’re making about someone’s life, based on their degree of perfection.”
—Juli Loesch (b. c. 1953)
“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 (1817–1862)
“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)