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:
“Nothing in life possesses value except the degree of power—assuming that life itself is the will to power.”
—Friedrich Nietzsche (1844–1900)
“In all pointed sentences, some degree of accuracy must be sacrificed to conciseness.”
—Samuel Johnson (1709–1784)
“Beat! beat! drums!—blow! bugles! blow!
Through the windows—through doors—burst like a ruthless force,
Into the solemn church, and scatter the congregation;
Into the school where the scholar is studying;
Leave not the bridegroom quiet—no happiness must he have now with his bride;
Nor the peaceful farmer any peace, plough his field or gathering his
grain;
So fierce you whirr and pound, you drums—so shrill you bugles blow.”
—Walt Whitman (1819–1892)
“Slavery is founded on the selfishness of man’s nature—opposition to it on his love of justice. These principles are in eternal antagonism; and when brought into collision so fiercely as slavery extension brings them, shocks and throes and convulsions must ceaselessly follow.”
—Abraham Lincoln (1809–1865)