Algorithmic and combinatorial algebra:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English Russian |
| Veröffentlicht: |
Dordrecht [u.a.]
Kluwer Acad. Publ.
1994
|
| Schriftenreihe: | Mathematics and its applications
255 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 349 - 379 |
| Beschreibung: | XVI, 384 S. |
| ISBN: | 0792323130 |
Internformat
MARC
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| 100 | 1 | |a Bokut', Leonid A. |d 1937- |e Verfasser |0 (DE-588)171983076 |4 aut | |
| 245 | 1 | 0 | |a Algorithmic and combinatorial algebra |c by L. A. Bokut' and G. P. Kukin |
| 264 | 1 | |a Dordrecht [u.a.] |b Kluwer Acad. Publ. |c 1994 | |
| 300 | |a XVI, 384 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Mathematics and its applications |v 255 | |
| 500 | |a Literaturverz. S. 349 - 379 | ||
| 650 | 7 | |a Algebra |2 gtt | |
| 650 | 7 | |a Algorithmes |2 ram | |
| 650 | 7 | |a Algoritmen |2 gtt | |
| 650 | 7 | |a Algèbre |2 ram | |
| 650 | 7 | |a Analyse combinatoire |2 ram | |
| 650 | 7 | |a Combinatieleer |2 gtt | |
| 650 | 4 | |a Algebra | |
| 650 | 4 | |a Algorithms | |
| 650 | 4 | |a Combinatorial analysis | |
| 650 | 0 | 7 | |a Algorithmus |0 (DE-588)4001183-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Algebra |0 (DE-588)4001156-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Kombinatorische Algebra |0 (DE-588)4735525-6 |2 gnd |9 rswk-swf |
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| 689 | 1 | 1 | |a Algorithmus |0 (DE-588)4001183-5 |D s |
| 689 | 1 | |5 DE-188 | |
| 700 | 1 | |a Kukin, G. P. |e Verfasser |4 aut | |
| 830 | 0 | |a Mathematics and its applications |v 255 |w (DE-604)BV008163334 |9 255 | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006420365&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-006420365 | ||
Datensatz im Suchindex
| _version_ | 1804124053851602944 |
|---|---|
| adam_text | Contents
Preface ix
1 Composition Method for Associative Algebras 1
1.1 Introduction 1
1.2 Free Semigroups and Free Groups 2
1.3 The Composition Lemma 5
1.4 The Composition Lemma for Semigroup Algebras 17
1.5 The Generalised Clifford Algebra and Some Other Examples 22
1.6 Finite Dimensional Representation of a Generalised Clifford Algebra 32
1.7 More on Embeddings into Simple Algebras 35
2 Free Lie Algebras 53
2.1 Introduction 53
2.2 The Definition of Free Lie Algebras 54
2.3 Projective Algebras 55
2.4 Elementary Transformations and Automorphisms of Free Algebras 56
2.5 Lie Algebra Derivations 57
2.6 The Ideal of Codimension 1 58
2.7 Constructing Generators for an Arbitrary Subalgebra in a Free Lie
Algebra 60
2.8 The Shirshov Theorem on Free Lie Algebra Subalgebras 61
2.9 Automorphisms of Free Lie Algebras of Finite Rank 64
2.10 A Criterion for a lie Algebra to be Free 65
2.11 Bases of a Free lie Algebra 66
2.12 Construction of Free Lie Algebras 73
2.13 Universal Enveloping Associative Algebra 74
2.14 On Subrings of Free Rings with Operators 76
2.15 Embedding Lie Rings into Associative Rings with Operators 84
2.16 Restricted Lie Algebras 86
2.17 Relatively Free Lie Algebras 90
2.18 Embedding Countable Dimensional lie Algebras into Lie Algebras
with Two Generators 92
2.19 The Residual Finiteness of Associative and Lie Algebras 94
2.20 Residual Finiteness of Free Rings and Algebras 101
v
vi
3 The Composition Method in the Theory of Lie Algebras 105
3.1 Introduction 105
3.2 The Composition Lemma 106
3.3 Formulation of Decision Problems. One Relator Lie Algebras 111
3.4 Embedding Lie Algebras into Simple Lie Algebras 118
3.5 The Main Algorithmic Problems for Lie Algebras are Unsolvable 120
3.6 Unrecognizable Markov Properties for Finitely Presented Lie
Algebras 123
3.7 Defining Relations of a Subalgebra 124
3.8 Residual Finiteness and Decision Problems 126
3.9 On Residual Finiteness of One Relator Lie Algebras 127
3.10 Constructing Free Resolutions 131
3.11 Cohomological Dimension of Almost Free Lie Algebras 134
4 Amalgamated Products of Lie Algebras 141
4.1 Introduction 141
4.2 Definition of Amalgamated Products 142
4.3 Constructing the Free Product of Associative Algebras without 1 143
4.4 Constructing the Amalgamated Product of Lie Algebras 144
4.5 Subalgebras of the Free Product of lie Algebras 146
4.6 Generators of a Subalgebra of the Free Product of Lie Algebras 147
4.7 Decomposition of a Free Product into the Sum of Two Subalgebras,
One Free 148
4.8 Decomposition of a Subalgebra of a Free Product into the Sum of
Two Subalgebras, One Free 151
4.9 The Theorem on Subalgebras of an Amalgamated Product of Lie
Algebras 152
4.10 Free Subalgebras in a Free Product of Lie Algebras 155
4.11 The Case in Which the Kurosh Formula Almost Holds 159
4.12 Supplementary Facts on Free Products 163
4.13 Residual Finiteness of Free Products of Associative and Lie
Algebras 167
4.14 Residual Finiteness of Free Soluble Lie Algebras with respect to
Inclusion into Finitely Generated Subalgebras 171
4.15 On Residual Finiteness of Free Soluble Groups with respect to
Inclusion into Finitely Generated Subgroups 172
4.16 On Residual Properties of Free Products of Lie Algebras. Central
Systems in Free Products 174
5 The Problem of Endomorph Reducibility and Relatively Free Groups
with the Word Problem Unsolvable 177
5.1 Introduction 177
5.2 When the Problem of Endomorph Reducibility for Relatively Free
Rings is Unsolvable 178
vii
5.3 When the Problem of Endomorph Reducibility is Solvable 182
5.4 The Problem of Endomorph Reducibility for Relatively Free Groups 185
5.5 The Variety R Included in Nc 188
5.6 The Free Group T of the Variety {A n N2)A2H and its Quotient
Group S 197
5.7 The Main Construction 199
5.8 Application to Constructing Non Finitely Based Varieties 202
5.9 An Interpretation of Polynomials 203
5.10 Unsolvability of Some Algorithmic Problems in the Theory of
Group 206
6 The Constructive Method in the Theory of HNN extensions. Groups
with Standard Normal Form 209
6.1 Introduction 209
6.2 Novikov Boone Groups 209
6.3 The Novikov Lemma and the Britton Lemma 215
6.4 The Definition of Groups with Standard Normal Form 218
6.5 The Novikov Group APiP2 222
6.6 The Boone Group 228
7 The Constructive Method for HNN extensions and the Conjugacy
Problem for Novikov Boone Groups 237
7.1 Introduction 237
7.2 The Conjugacy Problem for the Group G, 240
7.3 The Group G2 256
7.4 Some Calculuses 262
7.5 The Conjugacy Problem for the Group AP1P2 276
7.6 Auxiliary facts 309
Appendix 1 Calculations in Free Groups 315
Al.l The Hall Identities 315
A1.2 Generators of the Commutant of a Free Group 315
A1.3 Generators for the Terms of the Lowest Central Series 323
Appendix 2 Algorithmic Properties of the Wreath Products of Groups 325
A2.1 Embeddings 325
A2.2 Groups of Type F/N 327
A2.3 When the Conjugacy Problem for a Wreath Product is Solvable 330
A2.4 When the Conjugacy Problem for the Groups of Type F/N is
Solvable 334
Appendix 3 Survey of the Theory of Absolutely Free Algebras 335
A3.1 Introduction 335
A3.2 Free Groupoids 335
viii
A3.3 Constructing a Free Algebra 337
A3.4 Subalgebras of Free Algebras 337
A3.5 Properties of Subalgebras of a Free Algebra 338
A3.6 The Word Problem for £ algebras 340
A3.7 Properties of Ideals of a Free Algebra 343
A3.8 Elementary Theories of Free Algebras 346
A3.9 Endomorphisms and Automorphisms of Free Algebras 347
Bibliography 349
Index 380
|
| any_adam_object | 1 |
| author | Bokut', Leonid A. 1937- Kukin, G. P. |
| author_GND | (DE-588)171983076 |
| author_facet | Bokut', Leonid A. 1937- Kukin, G. P. |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
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| dewey-search | 512/.02 |
| dewey-sort | 3512 12 |
| dewey-tens | 510 - Mathematics |
| discipline | Informatik Mathematik |
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| id | DE-604.BV009706507 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:39:33Z |
| institution | BVB |
| isbn | 0792323130 |
| language | English Russian |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006420365 |
| oclc_num | 27976012 |
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| physical | XVI, 384 S. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
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| publisher | Kluwer Acad. Publ. |
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| series | Mathematics and its applications |
| series2 | Mathematics and its applications |
| spelling | Bokut', Leonid A. 1937- Verfasser (DE-588)171983076 aut Algorithmic and combinatorial algebra by L. A. Bokut' and G. P. Kukin Dordrecht [u.a.] Kluwer Acad. Publ. 1994 XVI, 384 S. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications 255 Literaturverz. S. 349 - 379 Algebra gtt Algorithmes ram Algoritmen gtt Algèbre ram Analyse combinatoire ram Combinatieleer gtt Algebra Algorithms Combinatorial analysis Algorithmus (DE-588)4001183-5 gnd rswk-swf Algebra (DE-588)4001156-2 gnd rswk-swf Kombinatorische Algebra (DE-588)4735525-6 gnd rswk-swf Kombinatorik (DE-588)4031824-2 gnd rswk-swf Algebra (DE-588)4001156-2 s Kombinatorik (DE-588)4031824-2 s Algorithmus (DE-588)4001183-5 s DE-604 Kombinatorische Algebra (DE-588)4735525-6 s DE-188 Kukin, G. P. Verfasser aut Mathematics and its applications 255 (DE-604)BV008163334 255 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006420365&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bokut', Leonid A. 1937- Kukin, G. P. Algorithmic and combinatorial algebra Mathematics and its applications Algebra gtt Algorithmes ram Algoritmen gtt Algèbre ram Analyse combinatoire ram Combinatieleer gtt Algebra Algorithms Combinatorial analysis Algorithmus (DE-588)4001183-5 gnd Algebra (DE-588)4001156-2 gnd Kombinatorische Algebra (DE-588)4735525-6 gnd Kombinatorik (DE-588)4031824-2 gnd |
| subject_GND | (DE-588)4001183-5 (DE-588)4001156-2 (DE-588)4735525-6 (DE-588)4031824-2 |
| title | Algorithmic and combinatorial algebra |
| title_auth | Algorithmic and combinatorial algebra |
| title_exact_search | Algorithmic and combinatorial algebra |
| title_full | Algorithmic and combinatorial algebra by L. A. Bokut' and G. P. Kukin |
| title_fullStr | Algorithmic and combinatorial algebra by L. A. Bokut' and G. P. Kukin |
| title_full_unstemmed | Algorithmic and combinatorial algebra by L. A. Bokut' and G. P. Kukin |
| title_short | Algorithmic and combinatorial algebra |
| title_sort | algorithmic and combinatorial algebra |
| topic | Algebra gtt Algorithmes ram Algoritmen gtt Algèbre ram Analyse combinatoire ram Combinatieleer gtt Algebra Algorithms Combinatorial analysis Algorithmus (DE-588)4001183-5 gnd Algebra (DE-588)4001156-2 gnd Kombinatorische Algebra (DE-588)4735525-6 gnd Kombinatorik (DE-588)4031824-2 gnd |
| topic_facet | Algebra Algorithmes Algoritmen Algèbre Analyse combinatoire Combinatieleer Algorithms Combinatorial analysis Algorithmus Kombinatorische Algebra Kombinatorik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006420365&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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