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:
“Words are made for a certain exactness of thought, as tears are for a certain degree of pain. What is least distinct cannot be named; what is clearest is unutterable.”
—René Daumal (19081944)
“The eloquence of one stimulates all the rest, some up to the speaking-point, and all others to a degree that makes them good receivers and conductors, and they avenge themselves for their enforced silence by increased loquacity on their return.”
—Ralph Waldo Emerson (18031882)
“The field of the poor may yield much food, but it is swept away through injustice.”
—Bible: Hebrew, Proverbs 13:23.
“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)