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:
“A certain degree of neurosis is of inestimable value as a drive, especially to a psychologist.”
—Sigmund Freud (1856–1939)
“A certain degree of ceremony is a necessary outwork of manners, as well as of religion; it keeps the forward and petulant at a proper distance, and is a very small restraint to the sensible and to the well-bred part of the world.”
—Philip Dormer Stanhope, 4th Earl Chesterfield (1694–1773)
“In the field of world policy I would dedicate this Nation to the policy of the Good Neighbor—the neighbor who resolutely respects himself and, because he does, respects the rights of others—the neighbor who respects his obligations and respects the sanctity of his agreements in and with a world of neighbors.”
—Franklin D. Roosevelt (1882–1945)
“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)