Improving the Fundamental Theorem of Algebra
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- Shipman, J. The Mathematical Intelligencer (2007) 29: 9. doi:10.1007/BF02986170
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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.