Modern Algebra and the Rise of Mathematical Structures

Authors: Corry, Leo

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About this book

The notion of a mathematical structure is among the most pervasive ones in twentieth-century mathematics. Modern Algebra and the Rise of Mathematical Structures describes two stages in the historical development of this notion: first, it traces its rise in the context of algebra from the mid-nineteenth century to its consolidation by 1930, and then it considers several attempts to formulate elaborate theories after 1930 aimed at elucidating, from a purely mathematical perspective, the precise meaning of this idea.

Part one dicusses the process whereby the aims and scope of the discipline of algebra were deeply transformed, turning it into that branch of mathematics dealing with a new kind of mathematical entities: the "algebraic structures". The transition from the classical, nineteenth-century, image of the discipline to the thear of ideals, from Richard Dedekind to Emmy Noether, and culminating with the publication in 1930 of Bartel L. van der Waerden's Moderne Algebra. Following its enormous success in algebra, the structural approach has been widely adopted in other mathematical domains since 1930s. But what is a mathematical structure and what is the place of this notion within the whole fabric of mathematics? Part Two describes the historical roots, the early stages and the interconnections between three attempts to address these questions from a purely formal, mathematical perspective: Oystein Ore's lattice-theoretical theory of structures, Nicolas Bourbaki's theory of structures, and the theory of categories and functors.

Table of contents (10 chapters)

  • Introduction: Structures in Mathematics

    Corry, Leo

    Pages 1-12

  • Structures in Algebra: Changing Images

    Corry, Leo

    Pages 19-63

  • Richard Dedekind: Numbers and Ideals

    Corry, Leo

    Pages 64-136

  • David Hilbert: Algebra and Axiomatics

    Corry, Leo

    Pages 137-182

  • Concrete and Abstract: Numbers, Polynomials, Rings

    Corry, Leo

    Pages 183-219

Buy this book

eBook $69.99
price for USA (gross)
  • ISBN 978-3-0348-7917-0
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $99.00
price for USA
  • ISBN 978-3-7643-7002-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Modern Algebra and the Rise of Mathematical Structures
Authors
Copyright
2004
Publisher
Birkhäuser Basel
Copyright Holder
Birkhäuser Verlag
eBook ISBN
978-3-0348-7917-0
DOI
10.1007/978-3-0348-7917-0
Softcover ISBN
978-3-7643-7002-2
Edition Number
2
Number of Pages
XVIII, 452
Additional Information
Originally published as volume 17 in the series: Science Networks Hist. Studies
Topics