Field Extension
In abstract algebra, field extensions are the main object of study in field theory. The general idea is to start with a base field and construct in some manner a larger field which contains the base field and satisfies additional properties. For instance, the set Q(√2) = {a + b√2 | a, b ∈ Q} is the smallest extension of Q which includes every real solution to the equation x2 = 2.
Read more about Field Extension: Definitions
Famous quotes containing the words field and/or extension:
“The frequent failure of men to cultivate their capacity for listening has a profound impact on their capacity for parenting, for it is mothers more than fathers who are most likely to still their own voices so they may hear and draw out the voices of their children.”
—Mary Field Belenky (20th century)
“Slavery is founded in the selfishness of man’s nature—opposition to it, is [in?] his love of justice.... Repeal the Missouri compromise—repeal all compromises—repeal the declaration of independence—repeal all past history, you still can not repeal human nature. It still will be the abundance of man’s heart, that slavery extension is wrong; and out of the abundance of his heart, his mouth will continue to speak.”
—Abraham Lincoln (1809–1865)