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)
“The birth of the new constitutes a crisis, and its mastery calls for a crude and simple cast of mind—the mind of a fighter—in which the virtues of tribal cohesion and fierceness and infantile credulity and malleability are paramount. Thus every new beginning recapitulates in some degree man’s first beginning.”
—Eric Hoffer (1902–1983)
“Yet, hermit and stoic as he was, he was really fond of sympathy, and threw himself heartily and childlike into the company of young people whom he loved, and whom he delighted to entertain, as he only could, with the varied and endless anecdotes of his experiences by field and river: and he was always ready to lead a huckleberry-party or a search for chestnuts and grapes.”
—Ralph Waldo Emerson (1803–1882)
“We know then the existence and nature of the finite, because we also are finite and have extension. We know the existence of the infinite and are ignorant of its nature, because it has extension like us, but not limits like us. But we know neither the existence nor the nature of God, because he has neither extension nor limits.”
—Blaise Pascal (1623–1662)