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.
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Famous quotes containing the words field and/or extension:
“The head must bow, and the back will have to bend,
Wherever the darkey may go;
A few more days, and the trouble all will end,
In the field where the sugar-canes grow.
A few more days for to tote the weary load,—
No matter, ‘t will never be light;
A few more days till we totter on the road:—
Then my old Kentucky home, good-night!”
—Stephen Collins Foster (1826–1884)
“Where there is reverence there is fear, but there is not reverence everywhere that there is fear, because fear presumably has a wider extension than reverence.”
—Socrates (469–399 B.C.)