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The Mathematical Intelligencer

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

Improving the Fundamental Theorem of Algebra

  • Joseph Shipman
Article

Conclusion

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.

Keywords

Galois Group Fundamental Theorem Mathematical Intelligencer Irreducible Polynomial Splitting Field 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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Copyright information

© Springer Science+Business Media, Inc 2007

Authors and Affiliations

  1. 1.Rocky HillUSA

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