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:
“But in every constitution some large degree of animal vigor is necessary as material foundation for the higher qualities of the art.”
—Ralph Waldo Emerson (1803–1882)
“Every man who attacks my belief, diminishes in some degree my confidence in it, and therefore makes me uneasy; and I am angry with him who makes me uneasy.”
—Samuel Johnson (1709–1784)
“In the quilts I had found good objects—hospitable, warm, with soft edges yet resistant, with boundaries yet suggesting a continuous safe expanse, a field that could be bundled, a bundle that could be unfurled, portable equipment, light, washable, long-lasting, colorful, versatile, functional and ornamental, private and universal, mine and thine.”
—Radka Donnell-Vogt, U.S. quiltmaker. As quoted in Lives and Works, by Lynn F. Miller and Sally S. Swenson (1981)
“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)