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 a, degree of, degree, field and/or extension:
“Never before has a civilization reached such a degree of a contempt for life; never before has a generation, drowned in mortification, felt such a rage to live.”
—Raoul Vaneigem (b. 1934)
“Wonderful “Force of Public Opinion!” We must act and walk in all points as it prescribes; follow the traffic it bids us, realise the sum of money, the degree of “influence” it expects of us, or we shall be lightly esteemed; certain mouthfuls of articulate wind will be blown at us, and this what mortal courage can front?”
—Thomas Carlyle (1795–1881)
“A new degree of intellectual power seems cheap at any price.”
—Ralph Waldo Emerson (1803–1882)
“... no young colored person in the United States today can truthfully offer as an excuse for lack of ambition or aspiration that members of his race have accomplished so little, he is discouraged from attempting anything himself. For there is scarcely a field of human endeavor which colored people have been allowed to enter in which there is not at least one worthy representative.”
—Mary Church Terrell (1863–1954)
“‘Tis the perception of the beautiful,
A fine extension of the faculties,
Platonic, universal, wonderful,
Drawn from the stars, and filtered through the skies,
Without which life would be extremely dull.”
—George Gordon Noel Byron (1788–1824)