However, we take the view that this is an opportunity for the student to grasp basic categorical notions which permeate so much of mathematics today, including, of course, algebraic topology, so that we do not allow ourselves to be rigidly restricted by our immediate objectives. A reader totally unfamiliar with category theory may find it easiest to restrict his first reading of Chapter II to Sections 1 to 6; large parts of the book are understandable with the material presented in these sections. Another reader, who had already met many examples of categorical formulations and concepts might, in fact, prefer to look at Chapter II before reading Chapter I. Of course the reader thoroughly familiar with category theory could, in principal, omit Chapter II, except perhaps to familiarize himself with the notations employed. It is shown how this group can be calculated by means of a projective presentation of A, or an injective presentation of B; and how it may also be identified with the group of equivalence classes of extensions of the quotient module A by the submodule B.

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I chose it because it was paperbound, and I thought it would be a good reference for students to own. Northcott, Introduction to Homological Algebra This was the first book on homological algebra I ever read, before I started graduate school. It is one of the most readable texts available, although some of the notation and terminology is now slightly out of date.

MacLane, Homology An excellent reference, and moderately readable. The title is misleading, since no topological aspects of homology are treated at all. Cartan and Eilenberg, Homological Algebra This was the book that started the whole subject, of course.

I remember how fascinated I was when I first saw it, since it seemed intriguing that one could apply topology to algebra. It should definitely not be considered obsolete. Jans, Rings and Homology A very small and somewhat intriguing book. The first chapter gives a nice readable treatment of the Wedderburn Theorem, suitable for beginners. The reminder of the book is more specialized and demands a greater sophistication from its readers.

Sharpe and Vamos, Injective Modules. I like this little book a whole lot. It brings in an assortment of subject matter from a whole lot of ring theory, both commutative and non-commutative, and finishes up by giving the complete classification of injective modules over commutative noetherian rings.

In my opinion, this is a good book from which to learn what algebra, and in particular module theory, is all about. I found it fairly easy to read once I learned to keep a pencil and paper handy, so that for each sentence in the book I could draw the corresponding diagram.

It should be called Categories for the Category Theorist. Matsumuta, Commutative Algebra This is certainly not an enjoyable book to read. But at the time I taught the course, it was the only book that treated most homological topics in commutative ring theory. There may be lots of more recent books which are excellent, for all I know. I basically lost interest in trying to keep up with these things about twenty years ago.

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About this book Introduction In this chapter we are largely influenced in our choice of material by the demands of the rest of the book. However, we take the view that this is an opportunity for the student to grasp basic categorical notions which permeate so much of mathematics today, including, of course, algebraic topology, so that we do not allow ourselves to be rigidly restricted by our immediate objectives. A reader totally unfamiliar with category theory may find it easiest to restrict his first reading of Chapter II to Sections 1 to 6; large parts of the book are understandable with the material presented in these sections. Another reader, who had already met many examples of categorical formulations and concepts might, in fact, prefer to look at Chapter II before reading Chapter I.

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## A course in homological algebra

However, we take the view that this is an opportunity for the student to grasp basic categorical notions which permeate so much of mathematics today, including, of course, algebraic topology, so that we do not allow ourselves to be rigidly restricted by our immediate objectives. A reader totally unfamiliar with category theory may find it easiest to restrict his first reading of Chapter II to Sections 1 to 6; large parts of the book are understandable with the material presented in these sections. Another reader, who had already met many examples of categorical formulations and concepts might, in fact, prefer to look at Chapter II before reading Chapter I. Of course the reader thoroughly familiar with category theory could, in principal, omit Chapter II, except perhaps to familiarize himself with the notations employed. It is shown how this group can be calculated by means of a projective presentation of A, or an injective presentation of B; and how it may also be identified with the group of equivalence classes of extensions of the quotient module A by the submodule B.

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## Homological algebra

Kazile Exact Couples and Spectral Sequences. In this holton edition, the authors have selected a number of different topics and describe some of the main applications and results to illustrate the range and depths of these developments. A Course in Homological Algebra P. Another reader, who had already met many examples of categorical formulations and concepts might, in fact, prefer to look at Chapter II before reading Chapter I.

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## HILTON STAMMBACH A COURSE IN HOMOLOGICAL ALGEBRA PDF

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