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Algebraic Theory of Complex Numbers
1962Before defining complex numbers let us briefly review the more familiar types of numbers and let us examine why there are different kinds of numbers.
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Algebraic Number Theory: Cyclotomy
2018In this chapter, we return to one of Gauss’s favourite themes, cyclotomic integers, and look at how they were used by Kummer, one of the leaders of the next generation of German number theorists. French and German mathematicians did not keep up-to-date with each other’s work, and for a brief, exciting moment in Paris in 1847 it looked as if the ...
Jeremy Gray, Jeremy Gray
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A Review of Number Theory and Algebra
2015Elementary number theory may be regarded as a prerequisite for this book, but since we, the authors, want to be nice to you, the readers, we provide a brief review of this theory for those who already have some background on number theory and a crash course on elementary number theory for those who have not.
Harald Niederreiter, Arne Winterhof
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Algebraic Identities in the Theory of Numbers
The American Mathematical Monthly, 1943(1943). Algebraic Identities in the Theory of Numbers. The American Mathematical Monthly: Vol. 50, No. 9, pp. 535-541.
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Algebraic Number Theory, A Survey
1982Publisher Summary This chapter explains algebraic number fields and its discreteness, factoring polynomials, valuation theory, unit theorem, and finiteness of class group and their proofs. Number theory is a good test for constructive mathematics as it applies to both discrete and continuous constructions; the constructive development brings to light
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Kronecker’s Algebraic Number Theory
2018In this chapter, we look at the Kroneckerian alternative to Dedekind’s approach to ‘ring theory’ set out in his Grundzuge and later extended by the Hungarian mathematician Gyula (Julius) Konig. This leads us to the emergence of the concept of an abstract field.
Jeremy Gray, Jeremy Gray
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Introduction to Algebraic Number Theory [PDF]
, 1982 By an algebraic number we mean a number 9 which is a root of the algebraic equation $$f(x) = a_n x^n + a_{n - 1} x^{n - 1} + \cdots + a_0 = 0,$$ (1)
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Primes and Algebraic Number Theory
2016The final major area within the theory of numbers is algebraic number theory. In this chapter we present an overview of the major ideas in this discipline. In line with the theme of these notes, we will concentrate on primes and prime decompositions.
Gerhard Rosenberger, Benjamin Fine
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The Birth of Algebraic Number Theory
2018In the first chapter we present the development of the theory of algebraic numbers in the 19th century, describing concisely the work of Gauss, Dirichlet, Eisenstein, Kummer, Hermite, Kronecker and Dedekind.
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