Linear algebra over commutative rings:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
New York [u.a.]
Dekker
1984
|
| Schriftenreihe: | Pure and applied mathematics
87 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000175233&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | VIII, 544 S. |
| ISBN: | 0824771222 |
Internformat
MARC
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| 100 | 1 | |a MacDonald, Bernard R. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Linear algebra over commutative rings |c Bernard R. McDonald |
| 264 | 1 | |a New York [u.a.] |b Dekker |c 1984 | |
| 300 | |a VIII, 544 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Pure and applied mathematics |v 87 | |
| 650 | 0 | 7 | |a Kommutativer Ring |0 (DE-588)4164825-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Lineare Algebra |0 (DE-588)4035811-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Matrizentheorie |0 (DE-588)4128970-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Matrixfunktion |0 (DE-588)4169117-9 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| DE-BY-TUM_call_number | 0102 MAT 150f 2001 A 24062 |
|---|---|
| DE-BY-TUM_katkey | 63000 |
| DE-BY-TUM_location | 01 |
| DE-BY-TUM_media_number | 040020264984 |
| _version_ | 1821939698762776577 |
| adam_text | Contents
PREFACE iii
I. MATRIX THEORY OVER COMMUTATIVE RINGS 1
A. The Polynomial Ring 1
B. Elementary Ideas 7
C. Ideals in (R)n 15
D. The Determinant 18
E. Matrices and Polynomials 31
F. The General Linear Group 44
1. Introduction to GLn(R) and Suslin s
Theorem 44
Appendix: Generators of SLn(R) 50
2. GLn(R), GLn(R[X]), and Similarity 56
3. Stable General Linear Group 67
4. Normal Subgroups and Automorphisms
of GLn(R) 73
(G) Systems of Linear Equations 79
II. FREE MODULES 97
A. Introduction 97
B. Free Modules and Their Morphisms 102
Appendix: Uniqueness of Basis Number 112
C. Fundamental Theorem of Projective Geometry 115
Appendix: The Projective Plane 126
D. Projective Modules 128
E. Change of Basis and Equivalence 135
III. THE ENDOMORPHISM RING OF A PROJECTIVE MODULE 153
A. Introduction 153
B. Category Correspondences and Free Modules 159
C. Duality and Projective Modules 181
1. Generators 181
2. Projectives 192
3. Morita Correspondence 195
D. Baer Correspondence 207
E. The Radical 215
vii
viii Contents
F. R Automorphisms of End^(P) 222
Appendix: Invertible Submodules,
Equivalence, and Isomorphisms of (R)n 241
IV. PROJECTIVE MODULES 250
A. Introduction 250
B. Spectrum of a Commutative Ring 250
C. Localization 256
D. Finitely Generated Modules 271
E. Finitely Generated Projective Modules 289
F. Stably Free Projective Modules 307
G. Projective Modules and Polynomial Rings 323
1. Completion of Unimodular Rows 339
2. Existence of Free Complements and K (R) 345
V. THEORY OF A SINGLE ENDOMORPHISM 359
A. Introduction 359
B. Tensor, Exterior, and Symmetric Algebras 360
1. The Tensor Algebra 360
2. The Exterior Algebra 366
3. The Symmetric Algebra 374
C. Exterior Algebras and Projective Modules 381
D. Exterior Algebras of Free Modules and a
Single Endomorphism 397
1. The Determinant of an Endomorphism 398
2. The Trace of an Endomorphism 407
3. The Characteristic Polynomial of
an Endomorphism 411
E. Theory of a Single Endomorphism of a
Projective Module 425
1. The Trace 425
2. The Determinant Trace Polynomial 430
3. The Determinant 435
4. The Characteristic Polynomial 440
F. Kq(R) and KQ(EndR) 448
1. The Ring K0(R) 450
2. X Rings and the Ring S2(R) 459
3. Ko(EndR) 467
G. A Theorem of Bass and the Koszul Complex 488
BIBLIOGRAPHY 505
INDEX 541
|
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| bvnumber | BV000288135 |
| classification_rvk | SK 230 |
| classification_tum | MAT 150f |
| ctrlnum | (OCoLC)251764399 (DE-599)BVBBV000288135 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV000288135 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T07:18:31Z |
| institution | BVB |
| isbn | 0824771222 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-000175233 |
| oclc_num | 251764399 |
| open_access_boolean | |
| owner | DE-12 DE-91G DE-BY-TUM DE-384 DE-739 DE-20 DE-29T DE-703 DE-11 DE-188 |
| owner_facet | DE-12 DE-91G DE-BY-TUM DE-384 DE-739 DE-20 DE-29T DE-703 DE-11 DE-188 |
| physical | VIII, 544 S. |
| publishDate | 1984 |
| publishDateSearch | 1984 |
| publishDateSort | 1984 |
| publisher | Dekker |
| record_format | marc |
| series | Pure and applied mathematics |
| series2 | Pure and applied mathematics |
| spellingShingle | MacDonald, Bernard R. Linear algebra over commutative rings Pure and applied mathematics Kommutativer Ring (DE-588)4164825-0 gnd Lineare Algebra (DE-588)4035811-2 gnd Matrizentheorie (DE-588)4128970-5 gnd Matrixfunktion (DE-588)4169117-9 gnd |
| subject_GND | (DE-588)4164825-0 (DE-588)4035811-2 (DE-588)4128970-5 (DE-588)4169117-9 |
| title | Linear algebra over commutative rings |
| title_auth | Linear algebra over commutative rings |
| title_exact_search | Linear algebra over commutative rings |
| title_full | Linear algebra over commutative rings Bernard R. McDonald |
| title_fullStr | Linear algebra over commutative rings Bernard R. McDonald |
| title_full_unstemmed | Linear algebra over commutative rings Bernard R. McDonald |
| title_short | Linear algebra over commutative rings |
| title_sort | linear algebra over commutative rings |
| topic | Kommutativer Ring (DE-588)4164825-0 gnd Lineare Algebra (DE-588)4035811-2 gnd Matrizentheorie (DE-588)4128970-5 gnd Matrixfunktion (DE-588)4169117-9 gnd |
| topic_facet | Kommutativer Ring Lineare Algebra Matrizentheorie Matrixfunktion |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000175233&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000001885 |
| work_keys_str_mv | AT macdonaldbernardr linearalgebraovercommutativerings |
Inhaltsverzeichnis
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Teilbibliothek Mathematik & Informatik
| Signatur: |
0102 MAT 150f 2001 A 24062 Lageplan |
|---|---|
| Exemplar 1 | Ausleihbar Am Standort |