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A course in modern algebra

Author: Peter Hilton; Yel-Chiang Wu
Publisher: New York, Wiley [1974]
Series: Pure and applied mathematics (John Wiley & Sons : Unnumbered)
Edition/Format:   Print book : EnglishView all editions and formats
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Additional Physical Format: Online version:
Hilton, Peter John.
Course in modern algebra.
New York, Wiley [1974]
(OCoLC)624981886
Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Peter Hilton; Yel-Chiang Wu
ISBN: 0471399671 9780471399674
OCLC Number: 730844
Notes: "A Wiley-Interscience publication."
Description: x, 249 pages illustrations 24 cm.
Contents: Groups. The definition of a group --
Subgroups --
Cosets, Lagrange's Theorem, and normal subgroups --
Homomorphisms --
Direct and free products --
Free groups and presentations --
Exact sequences --
Abelian groups. Special features of commutative groups --
Direct sums and products of Abelian groups : the structure of finitely generated Abelian groups --
Projective and injective Abelian groups --
Exact sequences of Abelian groups --
The tensor product of Abelian groups --
Categories and functors. Categories --
Functors --
Natural transformations --
Duality principle --
Products and coproducts --
Pullbacks and pushouts --
Adjoint functors --
Abelian categories --
Modules. Rings --
Modules --
The functor Hom --
The functor (x) --
Projective modules --
Injective modules --
Integral domains. Principal ideal domains --
Unique factorization domains --
Noetherian rings and modules --
Modules over principal ideal domains --
Semisimple rings. The Morita Theorem --
Semisimple rings --
The functors Ext and Tor. Chain complexes, chain maps, and homology --
Chain homotopy and the fundamental Lemmas --
The functor Ext --
The functor Tor --
Pullbacks and pushouts --
Ext and extensions.
Series Title: Pure and applied mathematics (John Wiley & Sons : Unnumbered)
Responsibility: [by] Peter Hilton [and] Yel-Chiang Wu.

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