Modern algebra and the rise of mathematical structures

Leo Corry

444 pages, parution le 25/03/2004 (2^eme édition)

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Résumé

The notion of mathematical structure is among the most pervasive ones in twentieth century mathematics. Modem 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 of the book discusses 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". 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.

The book is intended for historians of mathematics and mathematicians interested in the development of algebra and in the history of twentieth-century mathematics. It will also be read with interest by philosophers and historians of science concerned with the role of heuristic and contextual factors in the development of scientific ideas.

Sommaire

Structures in algebra: changing images
Richard Dedekind: numbers and ideals
David Hilbert: algebra and axiomatics
Concrete and abstract: numbers, polynomials, rings
Emmy Noether: ideals and structures
Oystein Ore: algebraic structures
Nicolas Bourbaki; theory of structures
Category theory: early stages
Categories and images of mathematics

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	PAPIER
Éditeur(s)	Birkhäuser
Auteur(s)	Leo Corry
Parution	25/03/2004
Édition	2^eme édition
Nb. de pages	444
Format	17 x 24
Couverture	Broché
Poids	1277g
Intérieur	Noir et Blanc
EAN13	9783764370022