Homological algebra. By Henri Cartan and Samuel Eilenberg. Prince- ton, The Princeton University Press, 15+ pp. $ At last this vigorous and. OK, I am looking at Cartan and Eilenberg Homological Algebra book (, printing). Chapter V.9, p97 they define functors T(-,-) of type L. Homological Algebra has now reached into almost every corner of modern mathematics. It started with the authored by H. Cartan and S. Eilenberg () [ 9].

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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. Visit the Help Desk. Now, looking at the proof of this proposition, they assume that A is a direct sum and C is a direct product and prove that T A,C is a direct product, which is correct. If you are a seller for this product, would you like to suggest updates through seller support? The invasion of algebra had occurred on three fronts through the construction of cohomology theories for groups, Lie algebras, and associative algebras.

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Subsequently, each of the three theories is singled out by a suitable specialization, and its specific properties are studied. Why read a text, especially as an introduction, whose notation and basic terminology is extinct? Here’s how restrictions apply.

By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service. Get to Know Us. Finally, a word about the 3-stars. Home Questions Tags Users Unanswered. Mathematics Stack Exchange works best with JavaScript enabled.

My problem is that I do not see the inner logic in their notation or definitions. Both were founding members of the Bourbaki and both received the Wolf Prize in Mathematics.


For those of you who are not new to the field then I am sure you already own your own copy, so enjoy.

Cartan–Eilenberg resolution

If not, somebody kindly enlighten me, I will treat you with a coffee which I myself may be missing, if I am not seeing this Be the first to review this item Amazon Bestsellers Rank: See all free Kindle reading apps. The starting point is the notion of a module over a ring. Share your thoughts with other customers. 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.

I must be completely missing the subtlety there for I am even at a loss with their claim that they “introduce the following FOUR types of functors” I see only two types. 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.

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Cartan and Eilenberg Homological Algebra – Mathematics Stack Exchange

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. Post as a guest Name. For those of you who are new to the field, my suggestion is to stay far away from this text. Princeton University Press; Algebbra ed. The primary operations are the tensor product of two catran and homoligical groups of all homomorphisms of one module into another. Earlier in the text, they have L and R as functors. Download one of the Free Kindle apps to start reading Kindle books on your smartphone, tablet, and computer.


In general, save your time and your money. That is certainly not correct. I cannot see logic in defining these two notions for the contravar, covar case. Thanks Makoto, for pointing out that they define it only for covar,contravar case.

It is time to give up the old and bring in the up to date and more relavent texts such as Weibel’s. Sign up using Facebook. I imagine L and R should stand for left and right. Sign up or log in Sign up using Google. Track your recent orders Use Your Account to view or change your orders. When this book was written, methods of algebraic topology had caused revolutions in the world of pure algebra.

If this is the error I think it is and a bad one toohas it been corrected subsequently and where? Would you like to tell us about a lower price? From these, “higher order” derived of operations are obtained, which enjoy all the properties usually attributed to homology theories. Post Your Answer Discard By clicking “Post Your Answer”, you acknowledge that you have read our homologiacl terms of serviceprivacy policy and cookie policyand that your continued use of the website is subject to these policies.

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.