Group Ring Groups. / Volume 1, : Orders and Generic Constructions of Units.
This two-volume graduate textbook gives a comprehensive, state-of-the-art account of describing large subgroups of the unit group of the integral group ring of a finite group and, more generally, of the unit group of an order in a finite dimensional semisimple rational algebra. Since the book is add...
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Place / Publishing House: | Berlin ;, Boston : : De Gruyter, , [2015] ©2016 |
Year of Publication: | 2015 |
Language: | English |
Series: | De Gruyter Textbook ;
Volume 1 |
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Physical Description: | 1 online resource (447 p.) |
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Jespers, Eric, author. aut http://id.loc.gov/vocabulary/relators/aut Group Ring Groups. Volume 1, Orders and Generic Constructions of Units. Berlin ; Boston : De Gruyter, [2015] ©2016 1 online resource (447 p.) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda De Gruyter Textbook ; Volume 1 Frontmatter -- Preface -- Contents -- 1. Units in group rings: an introduction -- 2. Representations of algebras -- 3. Wedderburn decomposition of semisimple group algebras -- 4. Dedekind domains, valuations and orders -- 5. The group of units of an order -- 6. Cyclotomic integers -- 7. Central units -- 8. Generic units -- 9. K-theory -- 10. General linear groups of degree 2 -- 11. Generators of the unit group of an integral group ring -- 12. Exceptional simple components -- 13. Idempotents and central units in group rings -- References -- Index of Notation -- Index restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star This two-volume graduate textbook gives a comprehensive, state-of-the-art account of describing large subgroups of the unit group of the integral group ring of a finite group and, more generally, of the unit group of an order in a finite dimensional semisimple rational algebra. Since the book is addressed to graduate students as well as young researchers, all required background on these diverse areas, both old and new, is included. Supporting problems illustrate the results and complete some of the proofs. Volume 1 contains all the details on describing generic constructions of units and the subgroup they generate. Volume 2 mainly is about structure theorems and geometric methods. Without being encyclopaedic, all main results and techniques used to achieve these results are included. Basic courses in group theory, ring theory and field theory are assumed as background. Mode of access: Internet via World Wide Web. In English. Description based on online resource; title from PDF title page (publisher's Web site, viewed 30. Aug 2021) Group rings Textbooks. Rings (Algebra) Textbooks Rings (Algebra) Textbooks. Unit groups (Ring theory) Textbooks. Gruppentheorie. MATHEMATICS / Group Theory. bisacsh del Río, Ángel, author. aut http://id.loc.gov/vocabulary/relators/aut Title is part of eBook package: De Gruyter DG Plus eBook-Package 2016 9783110701005 Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2015 9783110439687 ZDB-23-DGG Title is part of eBook package: De Gruyter EBOOK PACKAGE Mathematics 2015 9783110438765 ZDB-23-DMA EPUB 9783110386172 print 9783110372786 https://doi.org/10.1515/9783110372946 https://www.degruyter.com/isbn/9783110372946 Cover https://www.degruyter.com/cover/covers/9783110372946.jpg |
language |
English |
format |
eBook |
author |
Jespers, Eric, Jespers, Eric, del Río, Ángel, |
spellingShingle |
Jespers, Eric, Jespers, Eric, del Río, Ángel, Group Ring Groups. De Gruyter Textbook ; Frontmatter -- Preface -- Contents -- 1. Units in group rings: an introduction -- 2. Representations of algebras -- 3. Wedderburn decomposition of semisimple group algebras -- 4. Dedekind domains, valuations and orders -- 5. The group of units of an order -- 6. Cyclotomic integers -- 7. Central units -- 8. Generic units -- 9. K-theory -- 10. General linear groups of degree 2 -- 11. Generators of the unit group of an integral group ring -- 12. Exceptional simple components -- 13. Idempotents and central units in group rings -- References -- Index of Notation -- Index |
author_facet |
Jespers, Eric, Jespers, Eric, del Río, Ángel, del Río, Ángel, del Río, Ángel, |
author_variant |
e j ej e j ej r á d rá rád |
author_role |
VerfasserIn VerfasserIn VerfasserIn |
author2 |
del Río, Ángel, del Río, Ángel, |
author2_variant |
r á d rá rád |
author2_role |
VerfasserIn VerfasserIn |
author_sort |
Jespers, Eric, |
title |
Group Ring Groups. |
title_full |
Group Ring Groups. Volume 1, Orders and Generic Constructions of Units. |
title_fullStr |
Group Ring Groups. Volume 1, Orders and Generic Constructions of Units. |
title_full_unstemmed |
Group Ring Groups. Volume 1, Orders and Generic Constructions of Units. |
title_auth |
Group Ring Groups. |
title_alt |
Frontmatter -- Preface -- Contents -- 1. Units in group rings: an introduction -- 2. Representations of algebras -- 3. Wedderburn decomposition of semisimple group algebras -- 4. Dedekind domains, valuations and orders -- 5. The group of units of an order -- 6. Cyclotomic integers -- 7. Central units -- 8. Generic units -- 9. K-theory -- 10. General linear groups of degree 2 -- 11. Generators of the unit group of an integral group ring -- 12. Exceptional simple components -- 13. Idempotents and central units in group rings -- References -- Index of Notation -- Index |
title_new |
Group Ring Groups. |
title_sort |
group ring groups. orders and generic constructions of units. |
series |
De Gruyter Textbook ; |
series2 |
De Gruyter Textbook ; |
publisher |
De Gruyter, |
publishDate |
2015 |
physical |
1 online resource (447 p.) |
contents |
Frontmatter -- Preface -- Contents -- 1. Units in group rings: an introduction -- 2. Representations of algebras -- 3. Wedderburn decomposition of semisimple group algebras -- 4. Dedekind domains, valuations and orders -- 5. The group of units of an order -- 6. Cyclotomic integers -- 7. Central units -- 8. Generic units -- 9. K-theory -- 10. General linear groups of degree 2 -- 11. Generators of the unit group of an integral group ring -- 12. Exceptional simple components -- 13. Idempotents and central units in group rings -- References -- Index of Notation -- Index |
isbn |
9783110372946 9783110701005 9783110439687 9783110438765 9783110386172 9783110372786 |
callnumber-first |
Q - Science |
callnumber-subject |
QA - Mathematics |
callnumber-label |
QA251 |
callnumber-sort |
QA 3251.35 J47 42016 |
genre_facet |
Textbooks. Textbooks |
url |
https://doi.org/10.1515/9783110372946 https://www.degruyter.com/isbn/9783110372946 https://www.degruyter.com/cover/covers/9783110372946.jpg |
illustrated |
Not Illustrated |
dewey-hundreds |
500 - Science |
dewey-tens |
510 - Mathematics |
dewey-ones |
512 - Algebra |
dewey-full |
512.2 |
dewey-sort |
3512.2 |
dewey-raw |
512.2 |
dewey-search |
512.2 |
doi_str_mv |
10.1515/9783110372946 |
oclc_num |
940678146 |
work_keys_str_mv |
AT jesperseric groupringgroupsvolume1 AT delrioangel groupringgroupsvolume1 |
status_str |
n |
ids_txt_mv |
(DE-B1597)428812 (OCoLC)940678146 |
carrierType_str_mv |
cr |
title_part_txt |
Orders and Generic Constructions of Units. |
hierarchy_parent_title |
Title is part of eBook package: De Gruyter DG Plus eBook-Package 2016 Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2015 Title is part of eBook package: De Gruyter EBOOK PACKAGE Mathematics 2015 |
is_hierarchy_title |
Group Ring Groups. |
container_title |
Title is part of eBook package: De Gruyter DG Plus eBook-Package 2016 |
author2_original_writing_str_mv |
noLinkedField noLinkedField |
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