Homological algebra, because of its fundamental nature, is relevant to many branches of pure mathematics, including number theory, geometry, group theory and ring theory. Professor Northcott's aim is to introduce homological ideas and methods and to show some of the results which can be achieved. The early chapters provide the results needed to establish the theory of derived functors and to introduce torsion and extension functors. The new concepts are then applied to the theory of global dimensions, in an elucidation of the structure of commutative Noetherian rings of finite global dimension and in an account of the homology and cohomology theories of monoids and groups. A final section is devoted to comments on the various chapters, supplementary notes and suggestions for further reading. This book is designed with the needs and problems of the beginner in mind, providing a helpful and lucid account for those about to begin research, but will also be a useful work of reference for specialists. It can also be used as a textbook for an advanced course.
Sprache
Verlagsort
Zielgruppe
Für höhere Schule und Studium
Illustrationen
Worked examples or Exercises
Maße
Höhe: 228 mm
Breite: 152 mm
Gewicht
ISBN-13
978-0-521-05841-4 (9780521058414)
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Schweitzer Klassifikation
Preface; 1. Generalities concerning modules; 2. Tensor products and groups of homomorphisms; 3. Categories and functors; 4. Homology functors; 5. Projective and injective modules; 6. Derived functors; 7. Torsion and extension functors; 8. Some useful identities; 9. Commutative Noetherian rings of finite global dimension; 10. Homology and cohomology theories of groups and moniods; Notes; References; Index.
