Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-20T06:18:24.975Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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