Unit groups of classical rings:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Oxford
Clarendon Press
1988
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIV, 370 S. |
| ISBN: | 0198535570 |
Internformat
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV001862875 | ||
| 003 | DE-604 | ||
| 005 | 20180503 | ||
| 007 | t | ||
| 008 | 890912s1988 |||| 00||| eng d | ||
| 020 | |a 0198535570 |9 0-19-853557-0 | ||
| 035 | |a (OCoLC)17676935 | ||
| 035 | |a (DE-599)BVBBV001862875 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-12 |a DE-384 |a DE-739 |a DE-29T |a DE-19 |a DE-11 |a DE-188 |a DE-20 | ||
| 050 | 0 | |a QA247 | |
| 082 | 0 | |a 512/.4 |2 19 | |
| 084 | |a SK 230 |0 (DE-625)143225: |2 rvk | ||
| 084 | |a SK 260 |0 (DE-625)143227: |2 rvk | ||
| 100 | 1 | |a Karpilovsky, Gregory |d 1940- |e Verfasser |0 (DE-588)131816357 |4 aut | |
| 245 | 1 | 0 | |a Unit groups of classical rings |c Gregory Karpilovsky |
| 264 | 1 | |a Oxford |b Clarendon Press |c 1988 | |
| 300 | |a XIV, 370 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Anneaux (Algèbre) | |
| 650 | 7 | |a Anneaux (Algèbre) |2 ram | |
| 650 | 4 | |a Corps algébriques - Unités de mesure | |
| 650 | 7 | |a Corps algébriques |2 ram | |
| 650 | 4 | |a Groupes, Théorie des | |
| 650 | 7 | |a Groupes, Théorie des |2 ram | |
| 650 | 4 | |a Représentations de groupes | |
| 650 | 7 | |a Représentations de groupes |2 ram | |
| 650 | 4 | |a Algebraic fields |x Units | |
| 650 | 4 | |a Group theory | |
| 650 | 4 | |a Representations of groups | |
| 650 | 4 | |a Rings (Algebra) | |
| 650 | 0 | 7 | |a Ring |g Mathematik |0 (DE-588)4128084-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Einheit |g Mathematik |0 (DE-588)4151302-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Gruppentheorie |0 (DE-588)4072157-7 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Ring |g Mathematik |0 (DE-588)4128084-2 |D s |
| 689 | 0 | 1 | |a Gruppentheorie |0 (DE-588)4072157-7 |D s |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Ring |g Mathematik |0 (DE-588)4128084-2 |D s |
| 689 | 1 | 1 | |a Einheit |g Mathematik |0 (DE-588)4151302-2 |D s |
| 689 | 1 | |5 DE-604 | |
| 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=001231573&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-001231573 | ||
Datensatz im Suchindex
| _version_ | 1804116326091849728 |
|---|---|
| adam_text | Contents
Notation n
1 Introduction 1
1.1 Notation and terminology 1
1.2 Assumed results 2
2 Algebraic units 13
2.1 Finiteness of the class group 13
2.2 The Dirichlet Chevalley Hasse Unit Theorem 16
2.3 Existence of real and conjugate independent units 28
2.4 Units in quadratic fields 31
2.5 Units in pure cubic fields 44
3 The unit group of Z[eB] 65
3.1 Relations between the unit groups of l[en] and Z[en + £~ ] 65
3.2 Dirichlet L series and class number formulas 74
3.3 Cyclotomic units 81
3.4 Bass independence theorem 86
4 Multiplicative groups of fields 92
4.1 Multiplicative structure of some classical fields 92
4.2 Multiplicative groups of local fields 112
4.3 Intermediate fields 136
4.4 Kneser s theorem and related results 146
4.5 Fields with free multiplicative groups modulo torsion 154
4.6 Embedding groups 168
4.7 Multiplicative groups under field extensions 173
5 Multiplicative groups of division rings 179
5.1 Commutativity conditions 179
5.2 Subnormal subgroups: preliminary results 184
5.3 Subnormal subgroups: main theorems 190
5.4 Periodic multiplicative commutators 198
5.5 Periodic subnormal subgroups 201
5.6 Free subgroups 206
x Contents
6 Rings with cyclic unit groups 214
6.1 Finite commutative rings with a cyclic group of units 214
6.2 Rings with a cyclic group of units: the general case 218
7 Finite generation of unit groups 223
7.1 General results 223
7.2 Finitely generated extensions 229
7.3 The Whitehead group and stability theorem 234
7.4 Finite generation of GLn(R) 242
8 Unit groups of group rings 246
8.1 Definitions and elementary properties 246
8.2 Trace of idempotents 255
8.3 Units of finite order 258
8.4 Trivial units 267
8.5 Conjugacy of group bases 274
8.6 A description of U(1G), G dihedral of order 2p 280
8.7 Torsion free complements 292
8.8 Solvability and nilpotence of U(ZG) 310
8.9 Units in commutative group rings 317
Bibliography 350
Author index 366
Subject index 368
|
| any_adam_object | 1 |
| author | Karpilovsky, Gregory 1940- |
| author_GND | (DE-588)131816357 |
| author_facet | Karpilovsky, Gregory 1940- |
| author_role | aut |
| author_sort | Karpilovsky, Gregory 1940- |
| author_variant | g k gk |
| building | Verbundindex |
| bvnumber | BV001862875 |
| callnumber-first | Q - Science |
| callnumber-label | QA247 |
| callnumber-raw | QA247 |
| callnumber-search | QA247 |
| callnumber-sort | QA 3247 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 230 SK 260 |
| ctrlnum | (OCoLC)17676935 (DE-599)BVBBV001862875 |
| 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 |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02114nam a2200565 c 4500</leader><controlfield tag="001">BV001862875</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20180503 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">890912s1988 |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0198535570</subfield><subfield code="9">0-19-853557-0</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)17676935</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV001862875</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakddb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-12</subfield><subfield code="a">DE-384</subfield><subfield code="a">DE-739</subfield><subfield code="a">DE-29T</subfield><subfield code="a">DE-19</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-188</subfield><subfield code="a">DE-20</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA247</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">512/.4</subfield><subfield code="2">19</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 230</subfield><subfield code="0">(DE-625)143225:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 260</subfield><subfield code="0">(DE-625)143227:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Karpilovsky, Gregory</subfield><subfield code="d">1940-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)131816357</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Unit groups of classical rings</subfield><subfield code="c">Gregory Karpilovsky</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Oxford</subfield><subfield code="b">Clarendon Press</subfield><subfield code="c">1988</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XIV, 370 S.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Anneaux (Algèbre)</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Anneaux (Algèbre)</subfield><subfield code="2">ram</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Corps algébriques - Unités de mesure</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Corps algébriques</subfield><subfield code="2">ram</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Groupes, Théorie des</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Groupes, Théorie des</subfield><subfield code="2">ram</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Représentations de groupes</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Représentations de groupes</subfield><subfield code="2">ram</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Algebraic fields</subfield><subfield code="x">Units</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Group theory</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Representations of groups</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Rings (Algebra)</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Ring</subfield><subfield code="g">Mathematik</subfield><subfield code="0">(DE-588)4128084-2</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Einheit</subfield><subfield code="g">Mathematik</subfield><subfield code="0">(DE-588)4151302-2</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Gruppentheorie</subfield><subfield code="0">(DE-588)4072157-7</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Ring</subfield><subfield code="g">Mathematik</subfield><subfield code="0">(DE-588)4128084-2</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Gruppentheorie</subfield><subfield code="0">(DE-588)4072157-7</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="1" ind2="0"><subfield code="a">Ring</subfield><subfield code="g">Mathematik</subfield><subfield code="0">(DE-588)4128084-2</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2="1"><subfield code="a">Einheit</subfield><subfield code="g">Mathematik</subfield><subfield code="0">(DE-588)4151302-2</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001231573&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-001231573</subfield></datafield></record></collection> |
| id | DE-604.BV001862875 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:36:43Z |
| institution | BVB |
| isbn | 0198535570 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001231573 |
| oclc_num | 17676935 |
| open_access_boolean | |
| owner | DE-12 DE-384 DE-739 DE-29T DE-19 DE-BY-UBM DE-11 DE-188 DE-20 |
| owner_facet | DE-12 DE-384 DE-739 DE-29T DE-19 DE-BY-UBM DE-11 DE-188 DE-20 |
| physical | XIV, 370 S. |
| publishDate | 1988 |
| publishDateSearch | 1988 |
| publishDateSort | 1988 |
| publisher | Clarendon Press |
| record_format | marc |
| spelling | Karpilovsky, Gregory 1940- Verfasser (DE-588)131816357 aut Unit groups of classical rings Gregory Karpilovsky Oxford Clarendon Press 1988 XIV, 370 S. txt rdacontent n rdamedia nc rdacarrier Anneaux (Algèbre) Anneaux (Algèbre) ram Corps algébriques - Unités de mesure Corps algébriques ram Groupes, Théorie des Groupes, Théorie des ram Représentations de groupes Représentations de groupes ram Algebraic fields Units Group theory Representations of groups Rings (Algebra) Ring Mathematik (DE-588)4128084-2 gnd rswk-swf Einheit Mathematik (DE-588)4151302-2 gnd rswk-swf Gruppentheorie (DE-588)4072157-7 gnd rswk-swf Ring Mathematik (DE-588)4128084-2 s Gruppentheorie (DE-588)4072157-7 s DE-604 Einheit Mathematik (DE-588)4151302-2 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001231573&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Karpilovsky, Gregory 1940- Unit groups of classical rings Anneaux (Algèbre) Anneaux (Algèbre) ram Corps algébriques - Unités de mesure Corps algébriques ram Groupes, Théorie des Groupes, Théorie des ram Représentations de groupes Représentations de groupes ram Algebraic fields Units Group theory Representations of groups Rings (Algebra) Ring Mathematik (DE-588)4128084-2 gnd Einheit Mathematik (DE-588)4151302-2 gnd Gruppentheorie (DE-588)4072157-7 gnd |
| subject_GND | (DE-588)4128084-2 (DE-588)4151302-2 (DE-588)4072157-7 |
| title | Unit groups of classical rings |
| title_auth | Unit groups of classical rings |
| title_exact_search | Unit groups of classical rings |
| title_full | Unit groups of classical rings Gregory Karpilovsky |
| title_fullStr | Unit groups of classical rings Gregory Karpilovsky |
| title_full_unstemmed | Unit groups of classical rings Gregory Karpilovsky |
| title_short | Unit groups of classical rings |
| title_sort | unit groups of classical rings |
| topic | Anneaux (Algèbre) Anneaux (Algèbre) ram Corps algébriques - Unités de mesure Corps algébriques ram Groupes, Théorie des Groupes, Théorie des ram Représentations de groupes Représentations de groupes ram Algebraic fields Units Group theory Representations of groups Rings (Algebra) Ring Mathematik (DE-588)4128084-2 gnd Einheit Mathematik (DE-588)4151302-2 gnd Gruppentheorie (DE-588)4072157-7 gnd |
| topic_facet | Anneaux (Algèbre) Corps algébriques - Unités de mesure Corps algébriques Groupes, Théorie des Représentations de groupes Algebraic fields Units Group theory Representations of groups Rings (Algebra) Ring Mathematik Einheit Mathematik Gruppentheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001231573&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT karpilovskygregory unitgroupsofclassicalrings |