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:
“There is always a degree of ridicule that attends a disappointment, though often very unjustly, if the expectation was reasonably grounded; however, it is certainly most prudent not to communicate, prematurely, one’s hopes or one’s fears.”
—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)
“How sweet I roam’d from field to field
And tasted all the summer’s pride,
Till I the Prince of Love beheld
Who in the sunny beams did glide!”
—William Blake (1757–1827)
“We are now a nation of people in daily contact with strangers. Thanks to mass transportation, school administrators and teachers often live many miles from the neighborhood schoolhouse. They are no longer in daily informal contact with parents, ministers, and other institution leaders . . . [and are] no longer a natural extension of parental authority.”
—James P. Comer (20th century)