The Mathematical Intelligencer

, Volume 29, Issue 4, pp 9–14 | Cite as

Improving the Fundamental Theorem of Algebra

  • Joseph Shipman


Theorems 2 and 3 establish the minimum algebraic conditions necessary for a field to be algebraically closed, and they can therefore be said to “optimize” the Fundamental Theorem of Algebra. But each specific“degree implication” is a first-order consequence of the axioms for fields, and could have been discovered two centuries ago; the existence of these finitary relationships appears to have been unsuspected by practically everyone, with one important exception.


Galois Group Fundamental Theorem Mathematical Intelligencer Irreducible Polynomial Splitting Field 
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Copyright information

© Springer Science+Business Media, Inc 2007

Authors and Affiliations

  1. 1.Rocky HillUSA

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