Results 331 to 340 of about 11,618,175 (381)
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1997
We have now given two proofs of the Fundamental Theorem of Algebra. Both of these involved much more analysis (calculus) than algebra. The first relied on the analytic properties of two-variable real-valued functions from advanced calculus as well as the continuity of real polynomials while the second proof followed from the theory of complex analysis.
Benjamin Fine, Gerhard Rosenberger
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We have now given two proofs of the Fundamental Theorem of Algebra. Both of these involved much more analysis (calculus) than algebra. The first relied on the analytic properties of two-variable real-valued functions from advanced calculus as well as the continuity of real polynomials while the second proof followed from the theory of complex analysis.
Benjamin Fine, Gerhard Rosenberger
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Extensions of Difference Fields
American Journal of Mathematics, 1952of algebraic fields, that is, fields in the ordinary sense, onily if the characteristic p exceed 0. In this case an extension which is monadic in the sense just described may be produced by adjoining a p-th root not already in the field. Our purpose in this paper is to present in organized form the still rudimentary theory of these phenomena, and to ...
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Intuitionistic Fuzzy Algebraic Field Extensions
Lecture Notes in Networks and Systems, 2023M Elomari, Melliani S, Elomari M
exaly
On linearly Chinese field extensions
Communications in Algebra, 2021Cornelius Greither, Lucas Reis
exaly
Rank gain of Jacobians over number field extensions with prescribed Galois groups
Mathematische Nachrichten, 2023Bo-Hae Im, Joachim KÖNIG
exaly
1997
The general theory of extension of fields became possible only after creation of set theory by Dedekind, George Cantor (1845–1918), and Zermelo (1871–1953). It first appeared in the large, classical work of Ernst Steinitz (1871–1928) of 1910 Algebraische Theorie der Korper, Crelle Journal 137, 167–309.
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The general theory of extension of fields became possible only after creation of set theory by Dedekind, George Cantor (1845–1918), and Zermelo (1871–1953). It first appeared in the large, classical work of Ernst Steinitz (1871–1928) of 1910 Algebraische Theorie der Korper, Crelle Journal 137, 167–309.
openaire +1 more source