Group Identities On Units And Symmetric Units Of Group Rings
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Group Identities on Units and Symmetric Units of Group Rings
Author | : Gregory T Lee |
Publsiher | : Springer Science & Business Media |
Total Pages | : 196 |
Release | : 2010-08-19 |
Genre | : Mathematics |
ISBN | : 9781849965040 |
Download Group Identities on Units and Symmetric Units of Group Rings Book in PDF, Epub and Kindle
Let FG be the group ring of a group G over a field F. Write U(FG) for the group of units of FG. It is an important problem to determine the conditions under which U(FG) satisfies a group identity. In the mid 1990s, a conjecture of Hartley was verified, namely, if U(FG) satisfies a group identity, and G is torsion, then FG satisfies a polynomial identity. Necessary and sufficient conditions for U(FG) to satisfy a group identity soon followed. Since the late 1990s, many papers have been devoted to the study of the symmetric units; that is, those units u satisfying u* = u, where * is the involution on FG defined by sending each element of G to its inverse. The conditions under which these symmetric units satisfy a group identity have now been determined. This book presents these results for arbitrary group identities, as well as the conditions under which the unit group or the set of symmetric units satisfies several particular group identities of interest.
Polynomial Identities in Algebras
Author | : Onofrio Mario Di Vincenzo,Antonio Giambruno |
Publsiher | : Springer Nature |
Total Pages | : 421 |
Release | : 2021-03-22 |
Genre | : Mathematics |
ISBN | : 9783030631116 |
Download Polynomial Identities in Algebras Book in PDF, Epub and Kindle
This volume contains the talks given at the INDAM workshop entitled "Polynomial identites in algebras", held in Rome in September 2019. The purpose of the book is to present the current state of the art in the theory of PI-algebras. The review of the classical results in the last few years has pointed out new perspectives for the development of the theory. In particular, the contributions emphasize on the computational and combinatorial aspects of the theory, its connection with invariant theory, representation theory, growth problems. It is addressed to researchers in the field.
Rings Modules Algebras and Abelian Groups
Author | : Alberto Facchini,Evan Houston,Luigi Salce |
Publsiher | : CRC Press |
Total Pages | : 530 |
Release | : 2020-02-10 |
Genre | : Mathematics |
ISBN | : 0824750810 |
Download Rings Modules Algebras and Abelian Groups Book in PDF, Epub and Kindle
Rings, Modules, Algebras, and Abelian Groups summarizes the proceedings of a recent algebraic conference held at Venice International University in Italy. Surveying the most influential developments in the field, this reference reviews the latest research on Abelian groups, algebras and their representations, module and ring theory, and topological
Groups Rings and Group Rings
Author | : A. Giambruno,César Polcino Milies,Sudarshan K. Sehgal |
Publsiher | : American Mathematical Soc. |
Total Pages | : 283 |
Release | : 2009 |
Genre | : Mathematics |
ISBN | : 9780821847718 |
Download Groups Rings and Group Rings Book in PDF, Epub and Kindle
Represents the proceedings of the conference on Groups, Rings and Group Rings, held July 28 - August 2, 2008, in Ubatuba, Brazil. This title contains results in active research areas in the theory of groups, group rings and algebras (including noncommutative rings), polynomial identities, Lie algebras and superalgebras.
Groups Rings Group Rings and Hopf Algebras
Author | : Jeffrey Bergen,Stefan Catoiu,William Chin |
Publsiher | : American Mathematical Soc. |
Total Pages | : 277 |
Release | : 2017-04-24 |
Genre | : Associative rings and algebras -- Modules, bimodules and ideals -- Modules, bimodules and ideals |
ISBN | : 9781470428051 |
Download Groups Rings Group Rings and Hopf Algebras Book in PDF, Epub and Kindle
This volume contains the proceedings of the International Conference on Groups, Rings, Group Rings, and Hopf Algebras, held October 2–4, 2015 at Loyola University, Chicago, IL, and the AMS Special Session on Groups, Rings, Group Rings, and Hopf Algebras, held October 3–4, 2015, at Loyola University, Chicago, IL. Both conferences were held in honor of Donald S. Passman's 75th Birthday. Centered in the area of group rings and algebras, this volume contains a mixture of cutting edge research topics in group theory, ring theory, algebras and their representations, Hopf algebras and quantum groups.
Structure Theorems of Unit Groups
Author | : Eric Jespers,Ángel del Río |
Publsiher | : Walter de Gruyter GmbH & Co KG |
Total Pages | : 227 |
Release | : 2015-11-13 |
Genre | : Mathematics |
ISBN | : 9783110411508 |
Download Structure Theorems of Unit Groups Book in PDF, Epub and Kindle
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.
Orders and Generic Constructions of Units
Author | : Eric Jespers,Ángel del Río |
Publsiher | : Walter de Gruyter GmbH & Co KG |
Total Pages | : 459 |
Release | : 2015-11-13 |
Genre | : Mathematics |
ISBN | : 9783110372946 |
Download Orders and Generic Constructions of Units Book in PDF, Epub and Kindle
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.
Methods in Ring Theory
Author | : Vesselin Drensky |
Publsiher | : CRC Press |
Total Pages | : 328 |
Release | : 2021-02-28 |
Genre | : Mathematics |
ISBN | : 9781000657357 |
Download Methods in Ring Theory Book in PDF, Epub and Kindle
"Furnishes important research papers and results on group algebras and PI-algebras presented recently at the Conference on Methods in Ring Theory held in Levico Terme, Italy-familiarizing researchers with the latest topics, techniques, and methodologies encompassing contemporary algebra."