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Earn +20 ptsQ: Prove that a finite integral domain is a field?
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Is every field an integral domain?
Yes, every field is an integral domain.
Every finite division ring is a field?
correct.
What is the range of the function y x2 2x 4.?
The range depends on the domain. If the domain is the complex field, the range is also the whole of the complex field. If the domain is x = 0 then the range is 4.
What represent the surface integral of electric field intensity?
Electric flux.
Can one formally define a division ring as a field that isn't necessarily commutative?
wedderburn's little theorem says all finite division rings are commutative so they are fields. So if it is a finite division ring, then the answer is NO But for an infinite division ring... I think you can!
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