Almira, J. M. An application of the Gelfand-Mazur theorem: the fundamental theorem of algebra revisited. (English) Zbl 1093.12001 Divulg. Mat. 13, No. 2, 13-125 (2005). 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. Reviewer: Jacek Gilewicz (Marseille) Cited in 1 Document MSC: 12D05 Polynomials in real and complex fields: factorization 12D10 Polynomials in real and complex fields: location of zeros (algebraic theorems) Keywords:polynomials: zeros and factorization in \(\mathbb{C}\) PDFBibTeX XMLCite \textit{J. M. Almira}, Divulg. Mat. 13, No. 2, 13--125 (2005; Zbl 1093.12001) Full Text: EuDML