Book Description

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.

Customer Reviews (3)

Old - Antiquated
Yes, this is a landmark book and yes this book has served many a fine mathematician but, let's be honest here, this book is out dated.Since the creation of this book there have been both advances within the field and the core terminology has been agreed upon.Why read a text, especially as an introduction, whose notation and basic terminology is extinct?Yes, it is nice to go back and read the works of the masters, the pioneers and wrap yourself up in a nice warm blanket of original and new thought.Whereas, if your trying to learn the subject matter for your own benefit or for research reasons, then I would not recommend this text.For those of you who are new to the field, my suggestion is to stay far away from this text.Try L.R. Vermani's text or Rotmans text instead.For those of you who are not new to the field then I am sure you already own your own copy, so enjoy.Finally, a word about the 3-stars.Sure this text deserves 5 stars for being well written, for being a landmark text and for many other reasons but, this texts hay day has gone and went.It is time to give up the old and bring in the up to date and more relavent texts such as Weibel's.In general, save your time and your money.

A landmark, that's it.
As the title of the series suggests, this is another "landmark" inbooks of mathematics. In fact, this was the only book on homological algebra for a certain period of time. I don't think this is a fungus, but with other modern good textbooks available (Weibel, for example) I am not inclined to give it "five stars".

H. Cartan and S. Eilenberg are the authors
I believe this is volume #19 of the Princeton Math. Ser.entitled Homological Algebra. The authors are H. Cartan and S. Eilenberg. H. Cartan is one of E. Cartan's sons. ... Read more