Consequences For Galois Theory
This gives a general picture, and indeed a way of developing Galois theory (along lines exploited in Grothendieck's Galois theory). It can be shown that for separable extensions the radical is always {0}; therefore the Galois theory case is the semisimple one, of products of fields alone.
Read more about this topic: Tensor Product Of Fields
Famous quotes containing the words consequences for, consequences and/or theory:
“The horror of Gandhi’s murder lies not in the political motives behind it or in its consequences for Indian policy or for the future of non-violence; the horror lies simply in the fact that any man could look into the face of this extraordinary person and deliberately pull a trigger.”
—Mary McCarthy (1912–1989)
“If you are prepared to accept the consequences of your dreams ... then you must still regard America today with the same naive enthusiasm as the generations that discovered the New World.”
—Jean Baudrillard (b. 1929)
“In the theory of gender I began from zero. There is no masculine power or privilege I did not covet. But slowly, step by step, decade by decade, I was forced to acknowledge that even a woman of abnormal will cannot escape her hormonal identity.”
—Camille Paglia (b. 1947)