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A Development of Associative Algebra and an Algebraic Theory of Numbers, I
Mathematics Magazine, 1952in which if we denote a particular element by Ck, its immediate successor in this is CkJ, where k denotes a natural number and k' its immediate successor in the set of natural numbers. We then introduced in addition to these symbols the symbol + (called a plus sign); x (called a multiplication sign); and (, called a left parenthesis symbol; and ...
M. W. Weaver, H. S. Vandiver
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Algebraic properties of number theories
Israel Journal of Mathematics, 1975Among other things we prove the following. (A) A number theory is convex if and only if it is inductive. (B) No r.e. number theory has JEP. (C) No number theory has AP. We also give some information about the hard cores of number theories.
H. Simmons +3 more
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1991
This book originates from graduate courses given in Cambridge and London. It provides a brisk, thorough treatment of the foundations of algebraic number theory, and builds on that to introduce more advanced ideas. Throughout, the authors emphasise the systematic development of techniques for the explicit calculation of the basic invariants, such as ...
Martin J. Taylor, A. Fröhlich
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This book originates from graduate courses given in Cambridge and London. It provides a brisk, thorough treatment of the foundations of algebraic number theory, and builds on that to introduce more advanced ideas. Throughout, the authors emphasise the systematic development of techniques for the explicit calculation of the basic invariants, such as ...
Martin J. Taylor, A. Fröhlich
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Foundations of the Theory of Algebraic Numbers
Nature, 1932THIS is the first volume of Prof. Hancock's work and is intended as an introduction to the second volume. Its size shows that he is engaged in no light task. His object is to help in making the theory of algebraic numbers more accessible, more attractive, and less difficult.
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The Roots of Commutative Algebra in Algebraic Number Theory
Mathematics Magazine, 1995To put the issues in a broader context, these three number-theoretic problems were instrumental in the emergence of algebraic number theory-one of the two main sources of the modern discipline of commutative algebra.' The other source was algebraic geometry.
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Algebraic Aspects of Number Theory
2014Chapter 10 discusses some more interesting properties of integers, in particular, properties of prime numbers and primality testing by using the tools of modern algebra, which are not studied in Chap. 1. In addition, the applications of number theory, particularly those directed towards theoretical computer science, are presented.
Mahima Ranjan Adhikari, Avishek Adhikari
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On a problem in algebraic number theory
Mathematical Proceedings of the Cambridge Philosophical Society, 1996Let K be an algebraic number field. If q is a prime ideal of the ring of integers of K and α is a number of K prime to q then Mq(α) denotes the multiplicative group generated by α modulo q. In the paper [5] there is the remark: ‘We do not know whether for all a, b, c ∈ ℚ with abc ≠ 0, |a| ≠ 1,|b| ≠ 1,|c| ≠ 1 there exist infinitely many primes q with Mq
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Computational Algebra and Number Theory
1995Preface. 1: Calculating Growth Functions for Groups Using Automata M. Brazil. 2: The Minimal Faithful Degree of a Finite Commutative Inverse Semigroup S. Byleveld, D. Easdown. 3: Generalizations of the Todd-Coxeter Algorithm S. A. Linton. 4: Computing Left Kan Extensions Using the Todd-Coxeter Procedure M. Leeming, R. F. C. Walters. 5: Computing Finite
A. J. Van Der Poorten, Wieb Bosma
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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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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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