A Course in Modern AlgebraISBN: 9780471504054
264 pages
January 1989

This classic work is now available in an unabridged paperback edition. Hilton and Wu's unique approach brings the reader from the elements of linear algebra past the frontier of homological algebra. They describe a number of different algebraic domains, then emphasize the similarities and differences between them, employing the terminology of categories and functors. Exposition begins with set theory and group theory, and continues with coverage categories, functors, natural transformations, and duality, and closes with discussion of the two most fundamental derived functors of homological algebra, Ext and Tor.
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Partial table of contents:
GROUPS.
Cosets, Lagrange's Theorem, and Normal Subgroups.
Direct and Free Products.
ABELIAN GROUPS.
Special Features of Commutative Groups.
Exact Sequences of Abelian Groups.
CATEGORIES AND FUNCTORS.
Natural Transformations.
Duality Principle.
Adjoint Functors.
MODULES.
Rings.
The Functor Hom.
INTEGRAL DOMAINS.
SEMISIMPLE RINGS.
The Morita Theorem.
THE FUNCTORS EXT AND TOR.
List of Symbols.
Bibliography.
Index.
GROUPS.
Cosets, Lagrange's Theorem, and Normal Subgroups.
Direct and Free Products.
ABELIAN GROUPS.
Special Features of Commutative Groups.
Exact Sequences of Abelian Groups.
CATEGORIES AND FUNCTORS.
Natural Transformations.
Duality Principle.
Adjoint Functors.
MODULES.
Rings.
The Functor Hom.
INTEGRAL DOMAINS.
SEMISIMPLE RINGS.
The Morita Theorem.
THE FUNCTORS EXT AND TOR.
List of Symbols.
Bibliography.
Index.
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