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 never saw, heard, nor read, that the clergy were beloved in any nation where Christianity was the religion of the country. Nothing can render them popular, but some degree of persecution.”
—Jonathan Swift (1667–1745)
“So that if you would form a just judgment of what is of infinite importance to you not to be misled in,—namely, in what degree of real merit you stand ... call in religion and morality.—Look,—What is written in the law of God?—How readest thou?—Consult calm reason and the unchangeable obligations of justice and truth;Mwhat say they?”
—Laurence Sterne (1713–1768)
“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)
“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)