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A Multivariable form of the Fundamental Theorem of Algebra

Published online by Cambridge University Press:  20 November 2018

Pablo M. Salzberg
Pablo M. Salzberg*
Affiliation:
Departamento De Matemáticas Universidad Simon Bolivar, Caracas, Venezuela
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Abstract

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Let H(x) be a homogeneous polynomial in n indeterminates over an algebraically closed field K. A necesssary and sufficient condition is given for H(x) to admit a factorization of the form

a, b∈ Kn, and “∘” is the usual inner product. This condition involves the linear derivatives of H(x).

Keywords

12D0512E05
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 26 , Issue 3 , 01 September 1983 , pp. 271 - 272
Copyright
Copyright © Canadian Mathematical Society 1983

References

1. Birkhoff, G. and MacLane, S., A Survey of Modern Algebra, third edition, N.Y.: Macmillan, 1965.Google Scholar
2. Salzberg, P. M, The Minimal Generating Space of a Polynomial, Linear Algebra and its Applications, 36 (1981), 89-96.Google Scholar