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:
“Without being forgiven, released from the consequences of what we have done, our capacity to act would ... be confined to one single deed from which we could never recover; we would remain the victims of its consequences forever, not unlike the sorcerers apprentice who lacked the magic formula to break the spell.”
—Hannah Arendt (19061975)
“The medium is the message. This is merely to say that the personal and social consequences of any mediumthat is, of any extension of ourselvesresult from the new scale that is introduced into our affairs by each extension of ourselves, or by any new technology.”
—Marshall McLuhan (19111980)
“If my theory of relativity is proven correct, Germany will claim me as a German and France will declare that I am a citizen of the world. Should my theory prove untrue, France will say that I am a German and Germany will declare that I am a Jew.”
—Albert Einstein (18791955)