A Course in Homological Algebra / by P.J. Hilton, U. Stammbach.

Format:

Book

Author/Creator:

Hilton, P. J., author.

Stammbach, Urs, author.

Contributor:

SpringerLink (Online service)

Series:

Graduate texts in mathematics 2197-5612 ; 4.

Graduate Texts in Mathematics, 2197-5612 ; 4

Language:

English

Subjects (All):

Algebra.

Mathematics.

Local Subjects:

Algebra.

Mathematics.

Physical Description:

1 online resource (IX, 340 pages 1 illustrations).

Edition:

First edition 1971.

Contained In:

Springer Nature eBook

Place of Publication:

New York, NY : Springer New York : Imprint: Springer, 1971.

System Details:

text file PDF

Summary:

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. Of course the reader thoroughly familiar with category theory could, in principal, omit Chapter II, except perhaps to familiarize himself with the notations employed. In Chapter III we begin the proper study of homological algebra by looking in particular at the group ExtA(A, B), where A and Bare A-modules. 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.

Contents:

I. Modules

II. Categories and Functors

III. Extensions of Modules

IV. Derived Functors

V. The Künneth Formula

VI. Cohomology of Groups

VII. Cohomology of Lie Algebras

VIII. Exact Couples and Spectral Sequences

IX. Satellites and Homology.

Other Format:

Printed edition:

ISBN:

9781468499360

Access Restriction:

Restricted for use by site license.