Structure Theorems Of Unit Groups
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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 | : 9783110412758 |
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.
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.
Group Ring Groups
Author | : Eric Jespers,Ángel del Río |
Publsiher | : De Gruyter Textbook |
Total Pages | : 0 |
Release | : 2016 |
Genre | : Group rings |
ISBN | : 3110411490 |
Download Group Ring 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.
Group Ring Groups Orders and generic constructions of units
Author | : Eric Jespers,Ángel del Río |
Publsiher | : de Gruyter |
Total Pages | : 0 |
Release | : 2016 |
Genre | : Group rings |
ISBN | : 3110372789 |
Download Group Ring Groups 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."
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.
Algorithmic and Experimental Methods in Algebra Geometry and Number Theory
Author | : Gebhard Böckle,Wolfram Decker,Gunter Malle |
Publsiher | : Springer |
Total Pages | : 753 |
Release | : 2018-03-22 |
Genre | : Mathematics |
ISBN | : 9783319705668 |
Download Algorithmic and Experimental Methods in Algebra Geometry and Number Theory Book in PDF, Epub and Kindle
This book presents state-of-the-art research and survey articles that highlight work done within the Priority Program SPP 1489 “Algorithmic and Experimental Methods in Algebra, Geometry and Number Theory”, which was established and generously supported by the German Research Foundation (DFG) from 2010 to 2016. The goal of the program was to substantially advance algorithmic and experimental methods in the aforementioned disciplines, to combine the different methods where necessary, and to apply them to central questions in theory and practice. Of particular concern was the further development of freely available open source computer algebra systems and their interaction in order to create powerful new computational tools that transcend the boundaries of the individual disciplines involved. The book covers a broad range of topics addressing the design and theoretical foundations, implementation and the successful application of algebraic algorithms in order to solve mathematical research problems. It offers a valuable resource for all researchers, from graduate students through established experts, who are interested in the computational aspects of algebra, geometry, and/or number theory.
Number Theory
Author | : Henri Cohen |
Publsiher | : Springer Science & Business Media |
Total Pages | : 673 |
Release | : 2007-05-23 |
Genre | : Mathematics |
ISBN | : 9780387499222 |
Download Number Theory Book in PDF, Epub and Kindle
The central theme of this book is the solution of Diophantine equations, i.e., equations or systems of polynomial equations which must be solved in integers, rational numbers or more generally in algebraic numbers. This theme, in particular, is the central motivation for the modern theory of arithmetic algebraic geometry. In this text, this is considered through three of its most basic aspects. The book contains more than 350 exercises and the text is largely self-contained. Much more sophisticated techniques have been brought to bear on the subject of Diophantine equations, and for this reason, the author has included five appendices on these techniques.