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An application of the Gelfand-Mazur theorem: the fundamental theorem of algebra revisited. (English) Zbl 1093.12001

The fundamental theorem of algebra saying that every polynomial of degree \(n\) is decomposable as a product of \(n\) linear factors (monomials) is elementarily proved using a certain isometry of Banach algebras followed from the Gelfand-Mazur theorem.

MSC:

12D05 Polynomials in real and complex fields: factorization
12D10 Polynomials in real and complex fields: location of zeros (algebraic theorems)
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