Results 271 to 280 of about 635,864 (319)

Algebraic Number Theory and Fermat's Last Theorem

, 2001
Algebraic Methods Algebraic Background Rings and Fields Factorization of Polynomials Field Extensions Symmetric Polynomials Modules Free Abelian Groups Algebraic Numbers Algebraic Numbers Conjugates and Discriminants Algebraic Integers Integral Bases ...
I. Stewart, D. Tall
semanticscholar   +1 more source

On K 2 and Some Classical Conjectures in Algebraic Number Theory

, 1972
Let k be any field, and let kx be the multiplicative group of k. One of the several equivalent definitions of K2k is that K2k = (kx ?z kx)/J, where J is the subgroup of the tensor product generated by all elements a 0 b with a + b = 1.
J. Coates
semanticscholar   +1 more source

Algebraic Number Theory

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
openaire   +1 more source

Algebraic number theory

, 1963
1. (a) Find the norms of these ideals in OK : mOK , where m ∈ Z; (2, 1 + √ −5), where K = Q( √ −5); (2, 1 2 (1 + √ −7)), where K = Q( √ −7); (22, 2 + √ −7), where K = Q( √ −7); (22, 3 + √ −7), where K = Q( √ −7).
Edwin Weiss
semanticscholar   +1 more source

Algebraic properties of number theories

Israel Journal of Mathematics, 1975
Among 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, H. Simmons, Angus Macintyre, Angus Macintyre   +3 more
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A Brief Guide to Algebraic Number Theory: Frontmatter

, 2001
Preface 1. Numbers and ideals 2. Valuations 3. Special fields 4. Analytic methods 5. Class field theory Appendix Exercises Suggested further reading.
H. Swinnerton-Dyer
semanticscholar   +1 more source

Foundations of the Theory of Algebraic Numbers

Nature, 1932
THIS 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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On a problem in algebraic number theory

Mathematical Proceedings of the Cambridge Philosophical Society, 1996
Let 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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Algebraic Aspects of Number Theory

2014
Chapter 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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Algebraic Number Theory: Cyclotomy

2018
In 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
openaire   +2 more sources