On Gauss's first proof of the fundamental theorem of algebra

Authors:
S. M. Gersten and John R. Stallings

Journal:
Proc. Amer. Math. Soc. **103** (1988), 331-332

MSC:
Primary 20E05; Secondary 12-01

DOI:
https://doi.org/10.1090/S0002-9939-1988-0938691-3

MathSciNet review:
938691

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Abstract | References | Similar Articles | Additional Information

Abstract: Gauss's first proof of the Fundamental Theorem of Algebra is shown to be related to basic properties of free groups.

**[1]**C. F. Gauss,*Werke*, vol. 3, Georg Olms Verlag, Hildesheim and New York, 1973.**[2]**Richard Z. Goldstein and Edward C. Turner,*Applications of topological graph theory to group theory*, Math. Z.**165**(1979), no. 1, 1–10. MR**521516**, https://doi.org/10.1007/BF01175125**[3]**Steve Smale,*The fundamental theorem of algebra and complexity theory*, Bull. Amer. Math. Soc. (N.S.)**4**(1981), no. 1, 1–36. MR**590817**, https://doi.org/10.1090/S0273-0979-1981-14858-8**[4]**Shlomo Sternberg,*Lectures on differential geometry*, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1964. MR**0193578****[5]***A source book in mathematics, 1200–1800*, Edited by D. J. Struik, Harvard University Press, Cambridge, Mass., 1969. MR**0238647**

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1988-0938691-3

Keywords:
Free group,
polynomial

Article copyright:
© Copyright 1988
American Mathematical Society