| Title | On the impossibility of a fixed point proof of the fundamental theorem of algebra. Seminar on mathematical analysis |
| Authors | Alexandru Aleman |
| Publication | Seminar on mathematical analysis (Cluj-Napoca, 1985), |
| Year | 1985 |
| Pages | 157 - 161 |
| Document type | Article |
| Status | Published |
| Quality controlled | Yes |
| Language | eng |
| Abstract English | The author shows that the proofs of \n B. H. Arnold\en Amer. Math. Monthly 56 (1949), 465--466; MR0031725 (11,195h) and \n I. Niven\en ibid. 57 (1950), 246--248; MR0035738 (12,4c) of the fundamental theorem of algebra, based on the Brouwer fixed point theorem, are incomplete. Both Arnold and Niven recognized that the proofs are invalid, and they remarked that no easy remedy seems to save their proofs.<br> <br> In his note the author shows that it is impossible to prove the fundamental theorem of algebra using the method of these authors. |
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