A Course in Homological Algebra:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
New York, NY
Springer New York
1971
|
| Series: | Graduate Texts in Mathematics
4 |
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | 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. |
| Physical Description: | 1 Online-Ressource (IX, 340 p) |
| ISBN: | 9781468499360 9780387900339 |
| ISSN: | 0072-5285 |
| DOI: | 10.1007/978-1-4684-9936-0 |
Staff View
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| spelling | Hilton, P. J. Verfasser aut A Course in Homological Algebra by P. J. Hilton, U. Stammbach New York, NY Springer New York 1971 1 Online-Ressource (IX, 340 p) txt rdacontent c rdamedia cr rdacarrier Graduate Texts in Mathematics 4 0072-5285 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. Mathematics Mathematics, general Mathematik Homologische Algebra (DE-588)4160598-6 gnd rswk-swf 1\p (DE-588)4151278-9 Einführung gnd-content 2\p (DE-588)4123623-3 Lehrbuch gnd-content Homologische Algebra (DE-588)4160598-6 s 3\p DE-604 Stammbach, U. Sonstige oth https://doi.org/10.1007/978-1-4684-9936-0 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Hilton, P. J. A Course in Homological Algebra Mathematics Mathematics, general Mathematik Homologische Algebra (DE-588)4160598-6 gnd |
| subject_GND | (DE-588)4160598-6 (DE-588)4151278-9 (DE-588)4123623-3 |
| title | A Course in Homological Algebra |
| title_auth | A Course in Homological Algebra |
| title_exact_search | A Course in Homological Algebra |
| title_full | A Course in Homological Algebra by P. J. Hilton, U. Stammbach |
| title_fullStr | A Course in Homological Algebra by P. J. Hilton, U. Stammbach |
| title_full_unstemmed | A Course in Homological Algebra by P. J. Hilton, U. Stammbach |
| title_short | A Course in Homological Algebra |
| title_sort | a course in homological algebra |
| topic | Mathematics Mathematics, general Mathematik Homologische Algebra (DE-588)4160598-6 gnd |
| topic_facet | Mathematics Mathematics, general Mathematik Homologische Algebra Einführung Lehrbuch |
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