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A NOTE ON THE FUNDAMENTAL THEOREM OF ALGEBRA

Part of: General field theory

Published online by Cambridge University Press:  28 March 2018

MOHSEN ALIABADI Open the ORCID record for MOHSEN ALIABADI [Opens in a new window]
MOHSEN ALIABADI*
Affiliation:
Department of Mathematics, Statistics and Computer Science, University of Illinois, 851 S. Morgan St, Chicago, IL 60607, USA email maliab2@uic.edu
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Abstract

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The algebraic proof of the fundamental theorem of algebra uses two facts about real numbers. First, every polynomial with odd degree and real coefficients has a real root. Second, every nonnegative real number has a square root. Shipman [‘Improving the fundamental theorem of algebra’, Math. Intelligencer29(4) (2007), 9–14] showed that the assumption about odd degree polynomials is stronger than necessary; any field in which polynomials of prime degree have roots is algebraically closed. In this paper, we give a simpler proof of this result of Shipman.

Keywords

fundamental theorem of algebrafundamental theorem of Galois theoryperfect field

MSC classification

Secondary: 12E05: Polynomials (irreducibility, etc.)
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 97 , Issue 3 , June 2018 , pp. 382 - 385
Copyright
© 2018 Australian Mathematical Publishing Association Inc. 

References

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