Title Statements
- Full title :Fields and rings / Irving Kaplansky.
Edition Statements
- Publication Date:1972.
- Edition:2d ed
Publication Statements
- Publisher(s):University of Chicago Press
- Place of Publication:Chicago
- Language:eng
- Publication Date:1972.
The Physical Object
- Description:x, 206 pages ; : 21 cm.
Edition Identifiers
- ISBN:0226424502, 9780226424507, 0226424510, 9780226424514
- oclc:ocm00481423
- LC Classification:QA247
- Dewey Decimal:512/.3
Table of Contents
pt. I. Fields. Field extensions -- Ruler and compass constructions -- Foundations of Galois theory -- Normality and stability -- Splitting fields -- Radical extensions -- The trace and norm theorems -- Finite fields -- Simple extensions -- Cubic and quartic equations -- Separability -- Miscellaneous results on radical extensions -- Infinite algebraic extensions -- pt. II. Rings. The radical -- Primitive rings and the density theorem -- Semi-simple rings -- The Wedderburn principal theorem -- Theorems of Hopkins and Levitzki -- Primitive rings with minimal ideals and dual vector spaces -- Simple rings -- pt. III. Homological dimension. Dimension of modules -- Global dimension -- First theorem on change of rings -- Polynomial rings -- Second theorem on change of rings -- Third theorem on change of rings -- Localization -- Preliminary lemmas -- A regular ring has finite global dimension -- A local ring of finite global dimension is regular -- Injective modules -- The group of homomorphisms -- The vanishing of Ext -- Injective dimension.
Bibliografía e índice.
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