Free rings and their relations:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
London [u.a.]
Acad. Press
1985
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | London Mathematical Society: LMS monographs
19 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XXII, 588 S. |
| ISBN: | 0121791521 |
Internformat
MARC
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| 100 | 1 | |a Cohn, Paul M. |d 1924-2006 |e Verfasser |0 (DE-588)121230538 |4 aut | |
| 245 | 1 | 0 | |a Free rings and their relations |c P. M. Cohn |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a London [u.a.] |b Acad. Press |c 1985 | |
| 300 | |a XXII, 588 S. | ||
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Datensatz im Suchindex
| _version_ | 1804114946488795136 |
|---|---|
| adam_text | Contents
Page
Preface to the second edition vii
From the preface to the first edition ix
Note to the reader xvii
Some terminology, notations and conventions used throughout the book xviii
List of special notation xxi
CHAPTER 0 PRELIMINARIES 1
0.1 Matrix rings 1
0.2 Rank conditions on free modules 6
0.3 Projective modules 10
0.4 Hermite rings 15
0.5 The monoid of projectives 19
0.6 The matrix of definition of a module ..... 23
0.7 Eigenrings and centralizers 30
0.8 Groups and rings of fractions 34
0.9 Modules over Ore domains 46
0.10 Skew polynomial rings . ....... 50
0.11 Free associative algebras and tensor rings .... 59
Notes and comments 62
CHAPTER 1 FIRS, SEMIFIRS AND n FIRS ... 64
1.1 Dependence relations 64
1.2 Firs and a firs 71
1.3 Strong Gn rings 74
1.4 Homological properties of firs and semifirs .... 77
1.5 Further properties of n firs 80
1.6 Inert extensions 83
Notes and comments 85
CHAPTER 2 THE WEAK ALGORITHM ... 87
2.1 The division algorithm 87
2.2 The n term weak algorithm 94
xiii
xiv CONTENTS
2.3 The associated graded ring ....... 100
2.4 Weak algebra bases in filtered rings and free algebras . . 104
2.5 The Hilbert series of a filtered ring 107
2.6 The construction of rings with a weak algorithm . . . Ill
2.7 Generators and relations for GE2(K) 115
2.8 The 2 term weak algorithm 121
2.9 The inverse weak algorithm ....... 124
2.10 The transfinite weak algorithm ...... 138
2.11 Computation of the dependence number .... 143
Notes and comments 150
CHAPTER 3 FACTORIZATION 153
3.1 The commutative case ........ 153
3.2 Similarity in semifirs 158
3.3 Factorization in matrix rings over semifirs .... 164
3.4 Rigid factorizations ........ 170
3.5 Factorization in semifirs: a closer look ..... 177
3.6 The primary decomposition 184
Notes and comments 191
CHAPTER 4 RINGS WITH A DISTRIBUTIVE FACTOR
LATTICE 193
4.1 Distributive modules ........ 193
4.2 Distributive factor lattices 199
4.3 Conditions for a distributive factor lattice .... 204
4.4 Finite distributive lattices . . . . . . . 211
4.5 The factor lattice 215
4.6 Eigenrings 219
Notes and comments ........ 226
CHAPTER 5 MODULES OVER FIRS AND SEMIFIRS 227
5.1 Bound and unbound modules 227
5.2 Duality 232
5.3 Positive and negative modules over semifirs .... 235
5.4 The ranks of matrices 245
5.5 Sylvester domains 252
5.6 Stable inner rank and pseudo Sylvester domains . . . 261
5.7 The factorization of matrices over semifirs .... 265
5.8 A normal form for matrices over a free algebra . . . 272
CONTENTS XV
5.9 The specialization lemma 281
5.10 Ascending chain conditions 287
5.11 The intersection theorem for firs 294
Notes and comments 296
CHAPTER 6 CENTRALIZERS, SUBALGEBRAS AND
AUTOMORPHISMS 298
6.1 Commutative subrings and central elements in 2 firs . . 298
6.2 2 Firs with prescribed centre 305
6.3 The centre of a fir 309
6.4 Bounded elements in 2 firs 312
6.5 Free monoids 321
6.6 Subalgebras and ideals of free algebras 329
6.7 Centralizers in power series rings and in free algebras . . 337
6.8 Automorphisms of polynomial rings 341
6.9 Automorphisms of free algebras 352
6.10 Invariants in free algebras 362
6.11 The Galois correspondence 371
Notes and comments ........ 378
CHAPTER 7 SKEW FIELDS OF FRACTIONS . . 381
7.1 The rational closure of a homomorphism . . . . 381
7.2 The category of R fields and specializations .... 388
7.3 Matrix ideals 395
7.4 Prime matrix ideals 400
7.5 Fields of fractions 412
7.6 Numerators and denominators ...... 421
7.7 The depth 432
7.8 Centralizers in universal fields of fractions of firs . . . 437
7.9 Determinants and valuations 445
7.10 Localization of semifirs and firs 453
7.11 Universal localization: another route ..... 462
Notes and comments ........ 486
CHAPTER 8 PRINCIPAL IDEAL DOMAINS . . 489
8.1 The diagonal reduction for matrices over a principal ideal
domain. 489
8.2 Finitely generated modules over principal ideal domains . 492
8.3 Skew polynomial rings ........ 497
xvi CONTENTS
8.4 Theory of a single pseudo linear transformation . . . 503
8.5 Eigenvalues and algebraic matrices ..... 506
8.6 Algebraic skew field extensions 515
8.7 Laurent series and the Malcev Neumann construction. . 521
8.8 Iterated skew polynomial rings ...... 532
Notes and comments 538
APPENDIX
1. Lattice theory 540
2. Categories and homological algebra 544
Bibliography and author index ...... 557
Subject index 581
|
| any_adam_object | 1 |
| author | Cohn, Paul M. 1924-2006 |
| author_GND | (DE-588)121230538 |
| author_facet | Cohn, Paul M. 1924-2006 |
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| bvnumber | BV000493107 |
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| callnumber-label | QA251 |
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| callnumber-subject | QA - Mathematics |
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| classification_tum | MAT 169f |
| ctrlnum | (OCoLC)11728376 (DE-599)BVBBV000493107 |
| dewey-full | 512/.4 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.4 |
| dewey-search | 512/.4 |
| dewey-sort | 3512 14 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV000493107 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:14:48Z |
| institution | BVB |
| isbn | 0121791521 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-000304911 |
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| physical | XXII, 588 S. |
| publishDate | 1985 |
| publishDateSearch | 1985 |
| publishDateSort | 1985 |
| publisher | Acad. Press |
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| series | London Mathematical Society: LMS monographs |
| series2 | London Mathematical Society: LMS monographs |
| spelling | Cohn, Paul M. 1924-2006 Verfasser (DE-588)121230538 aut Free rings and their relations P. M. Cohn 2. ed. London [u.a.] Acad. Press 1985 XXII, 588 S. txt rdacontent n rdamedia nc rdacarrier London Mathematical Society: LMS monographs 19 Anneaux associatifs ram algèbre libre inriac anneau associatif inriac anneau idéal inriac théorie anneau inriac Associative rings Assoziativer Ring (DE-588)4143228-9 gnd rswk-swf Ring Mathematik (DE-588)4128084-2 gnd rswk-swf Freier Ring (DE-588)4155295-7 gnd rswk-swf Assoziativer Ring (DE-588)4143228-9 s DE-604 Freier Ring (DE-588)4155295-7 s Ring Mathematik (DE-588)4128084-2 s 1\p DE-604 London Mathematical Society: LMS monographs 19 (DE-604)BV026522023 19 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000304911&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Cohn, Paul M. 1924-2006 Free rings and their relations London Mathematical Society: LMS monographs Anneaux associatifs ram algèbre libre inriac anneau associatif inriac anneau idéal inriac théorie anneau inriac Associative rings Assoziativer Ring (DE-588)4143228-9 gnd Ring Mathematik (DE-588)4128084-2 gnd Freier Ring (DE-588)4155295-7 gnd |
| subject_GND | (DE-588)4143228-9 (DE-588)4128084-2 (DE-588)4155295-7 |
| title | Free rings and their relations |
| title_auth | Free rings and their relations |
| title_exact_search | Free rings and their relations |
| title_full | Free rings and their relations P. M. Cohn |
| title_fullStr | Free rings and their relations P. M. Cohn |
| title_full_unstemmed | Free rings and their relations P. M. Cohn |
| title_short | Free rings and their relations |
| title_sort | free rings and their relations |
| topic | Anneaux associatifs ram algèbre libre inriac anneau associatif inriac anneau idéal inriac théorie anneau inriac Associative rings Assoziativer Ring (DE-588)4143228-9 gnd Ring Mathematik (DE-588)4128084-2 gnd Freier Ring (DE-588)4155295-7 gnd |
| topic_facet | Anneaux associatifs algèbre libre anneau associatif anneau idéal théorie anneau Associative rings Assoziativer Ring Ring Mathematik Freier Ring |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000304911&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV026522023 |
| work_keys_str_mv | AT cohnpaulm freeringsandtheirrelations |