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 .
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“I never saw, heard, nor read, that the clergy were beloved in any nation where Christianity was the religion of the country. Nothing can render them popular, but some degree of persecution.”
—Jonathan Swift (1667–1745)
“Take but degree away, untune that string,
And hark what discord follows!
...
Force should be right, or, rather, right and wrong—
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Should lose their names, and so should justice too.
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—Abraham Lincoln (1809–1865)