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Hurwitz's Lectures on the Number Theory of Quaternions

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Title: Hurwitz's Lectures on the Number Theory of Quaternions
Description: Quaternions are non-commutative generalizations of the complex numbers, invented by William Rowan Hamilton in 1843. Their number-theoretical aspects were first investigated by Rudolf Lipschitz in the 1880s, and, in a streamlined form, by Adolf Hurwitz in 1896. This book contains an English translation of his 1919 textbook on this topic as well as his famous 1-2-3-4 theorem on composition algebras. In addition, the reader can find commentaries that shed historical light on the development of this number theory of quaternions, for example, the classical preparatory works (of Fermat, Euler, Lagrange and Gauss to name but a few), the different notions of quaternion integers in the works of Lipschitz and Hurwitz, analogies to the theory of algebraic numbers, and the further development (including Dickson's work in particular). The authors have implemented parts of the book in stand-alone courses, and they further believe that the present book can also complement well a course on algebraic number theory (with respect to a non-commutative extension of the rational numbers).
Authors: Nicola Oswald, Jörn Steuding
Resource Type: eBook.
Subjects: Number theory, Quaternions
Categories: MATHEMATICS / Number Theory
Database: eBook Collection (EBSCOhost)
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DbLabel: eBook Collection (EBSCOhost)
An: 3808239
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PubType: eBook
PubTypeId: ebook
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  Data: Hurwitz's Lectures on the Number Theory of Quaternions
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  Data: Quaternions are non-commutative generalizations of the complex numbers, invented by William Rowan Hamilton in 1843. Their number-theoretical aspects were first investigated by Rudolf Lipschitz in the 1880s, and, in a streamlined form, by Adolf Hurwitz in 1896. This book contains an English translation of his 1919 textbook on this topic as well as his famous 1-2-3-4 theorem on composition algebras. In addition, the reader can find commentaries that shed historical light on the development of this number theory of quaternions, for example, the classical preparatory works (of Fermat, Euler, Lagrange and Gauss to name but a few), the different notions of quaternion integers in the works of Lipschitz and Hurwitz, analogies to the theory of algebraic numbers, and the further development (including Dickson's work in particular). The authors have implemented parts of the book in stand-alone courses, and they further believe that the present book can also complement well a course on algebraic number theory (with respect to a non-commutative extension of the rational numbers).
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  Data: <searchLink fieldCode="AR" term="%22Nicola+Oswald%22">Nicola Oswald</searchLink><br /><searchLink fieldCode="AR" term="%22Jörn+Steuding%22">Jörn Steuding</searchLink>
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    Classifications:
      – Code: 510
        Scheme: ddc
        Type: prePub
    Languages:
      – Code: eng
        Text: English
    Subjects:
      – SubjectFull: Number theory
        Type: general
      – SubjectFull: Quaternions
        Type: general
    Titles:
      – TitleFull: Hurwitz's Lectures on the Number Theory of Quaternions
        Type: main
  BibRelationships:
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      – PersonEntity:
          Name:
            NameFull: Nicola Oswald
      – PersonEntity:
          Name:
            NameFull: Jörn Steuding
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            NameFull: Nicola Oswald
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          Name:
            NameFull: Jörn Steuding
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          Dates:
            – D: 01
              M: 01
              Type: published
              Y: 2023
            – D: 21
              M: 03
              Type: profile
              Y: 2024
          Identifiers:
            – Type: isbn-print
              Value: 9783985470112
            – Type: isbn-electronic
              Value: 9783985475117
          Titles:
            – TitleFull: Hurwitz's Lectures on the Number Theory of Quaternions
              Type: main
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