Homological Algebra (PMS-19), Volume 19

Henry Cartan

ISBN 10: 0691049912 / ISBN 13: 9780691049915

Published by Princeton University Press, 1999

About this Item

The invasion of algebra had occurred on three fronts through the construction of cohomology theories for groups, Lie algebras, and associative algebras. This book presents a single homology theory that embodies all three. Series: Princeton Mathematical Series. Num Pages: 408 pages, black & white illustrations. BIC Classification: PBF. Category: (P) Professional & Vocational; (U) Tertiary Education (US: College). Dimension: 229 x 152 x 21. Weight in Grams: 542. . 1999. Paperback. . . . . Books ship from the US and Ireland.

Seller Inventory # V9780691049915

Bibliographic Details

• Title: Homological Algebra (PMS-19), Volume 19
• Publisher: Princeton University Press
• Publication Date: 1999
• Language: English
• ISBN 10: 0691049912
• ISBN 13: 9780691049915
• Binding: Soft cover
• Condition: New

About this title

Synopsis

When this book was written, methods of algebraic topology had caused revolutions in the world of pure algebra. To clarify the advances that had been made, Cartan and Eilenberg tried to unify the fields and to construct the framework of a fully fledged theory. The invasion of algebra had occurred on three fronts through the construction of cohomology theories for groups, Lie algebras, and associative algebras. This book presents a single homology (and also cohomology) theory that embodies all three; a large number of results is thus established in a general framework. Subsequently, each of the three theories is singled out by a suitable specialization, and its specific properties are studied.


The starting point is the notion of a module over a ring. The primary operations are the tensor product of two modules and the groups of all homomorphisms of one module into another. From these, "higher order" derived of operations are obtained, which enjoy all the properties usually attributed to homology theories. This leads in a natural way to the study of "functors" and of their "derived functors."


This mathematical masterpiece will appeal to all mathematicians working in algebraic topology.

About the Author

Henri Cartan, formerly Professor of Mathematics at the University of Paris, is a Fellow of the Royal Society. Samuel Eilenberg (1914-1998) was Professor of Mathematics at Columbia University. Both were founding members of the Bourbaki and both received the Wolf Prize in Mathematics.