대수적 수론

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  1. This module is based on the book Algebraic Number Theory and Fermat's Last Theorem, by I.N. Stewart and D.O. Tall, published by A.K. Peters (2001).[1]
  2. These are four main problems in algebraic number theory, and answering them constitutes the content of algebraic number theory.[2]
  3. In order to overcome this difficulty Kummer introduced ideal numbers, thus altering the entire structure of algebraic number theory for the future.[2]
  4. This question led to class field theory, a central part of modern algebraic number theory.[2]
  5. In principle, this equation solves the third problem in algebraic number theory, but it is a local equation in the sense that it is necessary to check it for each prime ideal separately.[2]
  6. Readers are lead at a measured pace through the topics to enable a clear understanding of the pinnacles of algebraic number theory.[3]
  7. Algebraic number theory is a branch of number theory that uses the techniques of abstract algebra to study the integers, rational numbers, and their generalizations.[4]
  8. David Hilbert unified the field of algebraic number theory with his 1897 treatise Zahlbericht (literally "report on numbers").[4]
  9. Generalizing this simple result to more general rings of integers is a basic problem in algebraic number theory.[4]
  10. This spirit is adopted in algebraic number theory.[4]
  11. Despite this exacting program, the book remains an introduction to algebraic number theory for the beginner...[5]
  12. Algebraic number theory comprises the study of algebraic numbers: numbers that satisfy polynomial equations with rational coefficients.[6]
  13. The study of algebraic number theory goes back to the nineteenth century, and was initiated by mathematicians such as Kronecker, Kummer, Dedekind, and Dirichlet.[7]
  14. Some work over finite fields, where there are connections with algebraic number theory and applications to areas such as error-correcting codes.[7]
  15. The primary goal of this book is to present the essential elements of algebraic number theory, including the theory of normal extensions up through a glimpse of class field theory.[8]
  16. Next, some of the tools of algebraic number theory are introduced, such as ideals, discriminants and valuations.[8]
  17. It can be used by a beginner in algebraic number theory who wishes to see some of the true power and depth of the subject.[8]
  18. The book is a standard text for taught courses in algebraic number theory.[9]
  19. There follow two chapters that discuss the theme of unique factorization, which is central to any study of algebraic number theory.[10]
  20. These topics conform more closely to those that I think should be considered in a first course on algebraic number theory than do the ones covered in Trifković, particularly in one major respect.[10]
  21. Algebraic number theory is the branch of number theory that deals with algebraic numbers.[11]
  22. More recently, algebraic number theory has developed into the abstract study of algebraic numbers and number fields themselves, as well as their properties.[11]
  23. This is a 2001 account of Algebraic Number Theory, a field which has grown to touch many other areas of pure mathematics.[12]
  24. The purpose of this chapter is to abridge a big gap between elementary number theory and algebraic number theory with the emphasis on similarity of the material with that of linear algebra.[13]
  25. The course provides a thorough introduction to algebraic number theory.[14]
  26. Several books entitled `Algebraic number theory', such as those by Stewart & Tall, E. Weiss, S. Lang, J. Neukirch, or Cassels & Fröhlich, can also profitably be consulted.[14]
  27. This is an algebraic number theory course with aim to cover Class Field Theory.[15]
  28. Algebraic number theory is the part of number theory that uses methods from algebra to answer questions about integers in general and number fields in particular.[16]
  29. It provides a brisk, thorough treatment of the foundations of algebraic number theory, and builds on that to introduce more advanced ideas.[17]

소스

  1. ↑ MA3A6 Algebraic Number Theory
  2. ↑ 2.0 2.1 2.2 2.3 Algebraic number theory
  3. ↑ Algebraic Number Theory
  4. ↑ 4.0 4.1 4.2 4.3 Algebraic number theory
  5. ↑ Algebraic Number Theory
  6. ↑ MATH 842: Algebraic number theory
  7. ↑ 7.0 7.1 Brief Description of Algebraic Number Theory, Algebraic Geometry and Representation Theory
  8. ↑ 8.0 8.1 8.2 Number Theory: Algebraic Numbers and Functions
  9. ↑ Algebraic Number Theory
  10. ↑ 10.0 10.1 Algebraic Number Theory
  11. ↑ 11.0 11.1 Algebraic Number Theory -- from Wolfram MathWorld
  12. ↑ Brief guide algebraic number theory
  13. ↑ Linear algebraic approach to algebraic number theory
  14. ↑ 14.0 14.1 Algebraic Number Theory
  15. ↑ Algebraic Number Theory
  16. ↑ MMA350 Algebraic Number Theory, 7.5 credits
  17. ↑ Algebraic Number Theory | Number theory

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  • [{'LOWER': 'algebraic'}, {'LOWER': 'number'}, {'LEMMA': 'theory'}]
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