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 fear produces the same effects as rashness.”
—Philip Dormer Stanhope, 4th Earl Chesterfield (1694–1773)
“O, when degree is shaked,
Which is the ladder of all high designs,
The enterprise is sick. How could communities,
Degrees in schools, and brotherhoods in cities,
Peaceful commerce from dividable shores,
The primogeniture and due of birth,
Prerogative of age, crowns, scepters, laurels,
But by degree stand in authentic place?
Take but degree away, untune that string,
And hark what discord follows. Each thing meets
In mere oppugnancy.”
—William Shakespeare (1564–1616)
“Father calls me William, sister calls me Will,
Mother calls me Willie, but the fellers call me Bill!”
—Eugene Field (1850–1895)
“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)