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:
“In all pointed sentences, some degree of accuracy must be sacrificed to conciseness.”
—Samuel Johnson (17091784)
“In this world, only those people who have fallen to the lowest degree of humiliation, far below beggary, who are not just without any social consideration but are regarded by all as being deprived of that foremost human dignity, reason itselfonly those people, in fact, are capable of telling the truth. All the others lie.”
—Simone Weil (19091943)
“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 (15641616)
“Wynken and Blynken are two little eyes,
And Nod is a little head,
And the wooden shoe that sailed the skies
Is a wee ones trundle-bed.”
—Eugene Field (18501895)
“Slavery is founded in the selfishness of mans natureopposition to it, is [in?] his love of justice.... Repeal the Missouri compromiserepeal all compromisesrepeal the declaration of independencerepeal all past history, you still can not repeal human nature. It still will be the abundance of mans heart, that slavery extension is wrong; and out of the abundance of his heart, his mouth will continue to speak.”
—Abraham Lincoln (18091865)