Improving the Fundamental Theorem of Algebra |
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Authors: | Joseph Shipman |
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Affiliation: | 1.Rocky Hill,USA |
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Abstract: | 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. |
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