Re: [HM] The Fundamental Theorem of Algebra

Sanford L. Segal (ssgl@math.rochester.edu)
Fri, 6 Nov 1998 17:11:19 -0500

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I am grateful to Gerhard Warnecke for his detailed remarks on the
literature of the Fundamental Theorem of Algebra. Let me just remark that
the essentially topological nature of FTA is also demonstrated by its
generalization to quaternions (or for that matter any non-commutative
division algebra) by Ivan Niven (using work of Ore and Baer) in American
Mathematical Monthly 48, 1941, 654-661, and by the fact that Laura Weiss in
a Ph.D. dissertation at the University of Rochester (1973) generalized it
to abstract topological structures called "Gamma Structures". I do not
know whether Weiss' work was ever published.
As to whether the unavoidable "non-algebraic" portion of the usual
FTA over the complex numbers is called analysis or topology seems
irrelevant: "Name sind Schall und Rauch".
Sanford Segal

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