An Introduction to Homological Algebra

NORTHCOTT (Autor)

Buch | Softcover

300 Seiten

2009
Cambridge University Press (Verlag)
978-0-521-09793-2 (ISBN)

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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.

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.

Erscheint lt. Verlag	8.1.2009
Zusatzinfo	Worked examples or Exercises
Verlagsort	Cambridge
Sprache	englisch
Maße	152 x 229 mm
Gewicht	440 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Algebra
ISBN-10	0-521-09793-2 / 0521097932
ISBN-13	978-0-521-09793-2 / 9780521097932
Zustand	Neuware