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:
“She is as in a field a silken tent
At midday when a sunny summer breeze
Has dried the dew and all its ropes relent,”
—Robert Frost (1874–1963)
“The motive of science was the extension of man, on all sides, into Nature, till his hands should touch the stars, his eyes see through the earth, his ears understand the language of beast and bird, and the sense of the wind; and, through his sympathy, heaven and earth should talk with him. But that is not our science.”
—Ralph Waldo Emerson (1803–1882)