Modern Algebra and the Rise of Mathematical StructuresBirkhäuser, 6 de des. 2012 - 452 pàgines The book describes two stages in the historical development of the notion of mathematical structures: 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. First published in the series Science Networks Historical Studies, Vol. 17 (1996). In the second rev. edition the author has eliminated misprints, revised the chapter on Richard Dedekind, and updated the bibliographical index. |
Continguts
| 1 | |
| 13 | |
Changing Images | 19 |
Numbers and Ideals | 64 |
Algebra and Axiomatics | 137 |
Ideals and Structures | 220 |
Structures in the Body of Mathematics 253 | 252 |
Algebraic Structures | 259 |
Theory of Structures | 289 |
Early Stages | 339 |
Categories and Images of Mathematics | 380 |
Bibliography | 399 |
| 433 | |
| 441 | |
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Frases i termes més freqüents
abstract algebra abstract rings alge algebraic geometry algebraic integers algebraic number algebraic number theory algebraic structures appear axiomatic axioms basic Boolean algebras Bourbaki category theory central chapter complex numbers concepts considered contained decomposition Dedekind defined definition detail Dieudonné discipline discussed Eilenberg elements Emmy Noether existence explicitly fact factorization fields finite formulation Fraenkel framework functors Galois theory geometry given Göttingen group theory Hensel Hilbert ideas image of algebra images of knowledge images of mathematics introduced invariant isomorphism Jordan-Hölder theorem kind Kummer later lattice Mac Lane mathematical structure mathematicians mentioned Moderne Algebra modules morphisms number theory Ore's program p-adic particular polynomials present primary ideals prime ideals problem proof properties proved published question rational real numbers role Steinitz struc structural approach structural image textbook theorem theory of ideals Theory of Sets theory of structures tion topology universal algebra Waerden's Weber