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:
“Essential truth, the truth of the intellectualists, the truth with no one thinking it, is like the coat that fits tho no one has ever tried it on, like the music that no ear has listened to. It is less real, not more real, than the verified article; and to attribute a superior degree of glory to it seems little more than a piece of perverse abstraction-worship.”
—William James (1842–1910)
“I still lack to a considerable degree that naturally superior kind of manner that I would dearly like to possess.”
—Heinrich Himmler (1900–1945)
“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)
“Predatory capitalism created a complex industrial system and an advanced technology; it permitted a considerable extension of democratic practice and fostered certain liberal values, but within limits that are now being pressed and must be overcome. It is not a fit system for the mid- twentieth century.”
—Noam Chomsky (b. 1928)