Weierstrass, Frobenius proofs
- From: rtrato@xxxxxxxxx
- Date: 15 Mar 2007 03:18:04 -0700
Can someone post a copy of the original proofs about the commutative
extension of the real number system?
I have been searching the web, but the best I found was this:
"In 1878, Frobenius proved that the quaternions were the only possible
(finite-dimensional) associative extension of the complex numbers in
which division was possible and the only (finite-dimensional) non-
commutative extension of the real numbers in which division was
possible. This was independently proved two years later by C. S.
Pierce. (Gauss had been convinced that the field of complex numbers
was the only finite dimensional commutative field extension of the
real number system. This was subsequently proved by Weierstrass",
quoted from: http://www.math.hawaii.edu/~lee/algebra/history.html
"Weierstrass, in his 1863 lectures proved that the complex numbers are
the only commutative algebraic extension of the real numbers. Gauss
had promised a proof of this in 1831 but had failed to give one. ",
quoted from http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Weierstrass.html
Also, look at: http://projecteuclid.org/Dienst/UI/1.0/Summarize/euclid.ndjfl/1093894626
, Weierstrass's final theorem of arithmetic is not final.
.
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