algebraic extension oor Koreaans
algebraic extension
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Krull's first publications were on rings and algebraic extension fields.
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The problem which he solved was whether, given an algebraically closed field O , there exist subfields K , properly contained in O , with O an algebraic extension of finite degree of its subfield K .
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His work on algebra was an extension of Abel's work on algebraic functions and their integrals.
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Hilbert's problems included the continuum hypothesis , the well ordering of the reals, Goldbach's conjecture , the transcendence of powers of algebraic numbers , the Riemann hypothesis , the extension of Dirichlet 's principle and many more.
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In Vorlesungen über die Algebra der Logik, a large work published between 1890 and 1905 (it was completed by E. Müller after his death), Schröder gave a detailed account of algebraic logic, provided a source for Tarski to develop the modern algebraic theory and gave an extensive bibliography of the history of logic.
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He possessed by far the most extensive collection of American texts on algebra and arithmetic, so it was natural for him to publish a work called Notes on the history of American textbooks on arithmetic in 1899.
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The ground covered in this book is very extensive: almost every topic of the classical algebro-geometric theory of algebraic curves, surfaces and varieties is discussed, or at least briefly mentioned, in the course of the exposition.
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The distinctive characteristic of the Analytical Engine, and that which has rendered it possible to endow mechanism with such extensive faculties as bid fair to make this engine the executive right-hand of abstract algebra, is the introduction into it of the principle which Jacquard devised for regulating, by means of punched cards, the most complicated patterns in the fabrication of brocaded stuffs.
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This wasn't the only book which published in 1983 for Central extensions, Galois groups, and ideal class groups of number fields appeared in the same year as did Gauss sums and p-adic division algebras with Classgroups and Hermitian modules being published in the following year.
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