Fields and Rings

Couverture
University of Chicago Press, 1972 - 206 pages
This book combines in one volume Irving Kaplansky's lecture notes on the theory of fields, ring theory, and homological dimensions of rings and modules.

"In all three parts of this book the author lives up to his reputation as a first-rate mathematical stylist. Throughout the work the clarity and precision of the presentation is not only a source of constant pleasure but will enable the neophyte to master the material here presented with dispatch and ease."—A. Rosenberg, Mathematical Reviews
 

Avis des internautes - Rédiger un commentaire

Aucun commentaire n'a été trouvé aux emplacements habituels.

Pages sélectionnées

Table des matières

FIELDS
2
1 Field Extensions
3
2 Ruler and compass constructions
9
3 Foundations of Galois theory
11
4 Normality and stability
20
5 Splitting fields
24
6 Radical extensions
33
7 The trace and norm theorems
40
7 Simple rings
148
2 Tensor products
151
3 Maximal subfields
155
4 Polynomial identities
157
5 Extension of isomorphisms
162
HOMOLOGICAL DIMENSION
166
1 Dimension of modules
168
2 Global dimension
172

8 Finite fields
46
9 Simple extensions
49
10 Cubic and quartic equations
51
11 Separability
56
12 Miscellaneous results on radical extensions
61
13 Infinite algebraic extensions
75
RINGS
80
1 The Radical
82
2 Primitive rings and the density theorem
92
3 Semisimple rings
108
4 The Wedderburn principal theorem
125
5 Theorems of Hopkins and Levitzki
133
6 Primitive rings with minimal ideals and dual vector spaces
140
4 Polynomial rings
175
5 Second theorem on change of rings
177
6 Third theorem on change of rings
178
7 Localization
182
8 Preliminary lemmas
183
9 A regular local ring has finite global dimension
184
11 Injective modules
186
12 The group of homomorphisms
188
14 Injective dimension
191
NOTES
194
INDEX
202
Droits d'auteur

Autres éditions - Tout afficher

Expressions et termes fréquents

À propos de l'auteur (1972)

Irving Kaplansky is Director Emeritus of the Mathematical Sciences Research Institute and George Herbert Mead Distinguished Service Professor Emeritus in the Department of Mathematics at the University of Chicago.

Informations bibliographiques