Ebook: Units in Skew Fields

This book is devoted to a study of the unit groups of orders in skew fields, finite dimensional and central over the rational field; it thereby belongs to the field of noncommutative arithmetic. Its purpose is a synopsis of results and methods, including full proofs of the most important results. It is addressed to researchers in number theory and arithmetic groups.

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This book is devoted to a study of the unit groups of orders in skew fields, finite dimensional and central over the rational field; it thereby belongs to the field of noncommutative arithmetic. Its purpose is a synopsis of results and methods, including full proofs of the most important results. It is addressed to researchers in number theory and arithmetic groups.

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This book is devoted to a study of the unit groups of orders in skew fields, finite dimensional and central over the rational field; it thereby belongs to the field of noncommutative arithmetic. Its purpose is a synopsis of results and methods, including full proofs of the most important results. It is addressed to researchers in number theory and arithmetic groups.
Content:
Front Matter....Pages i-viii
Basic Facts....Pages 1-4
Hey’s Theorem and Consequences....Pages 5-7
Siegel-Weyl Reduction Theory....Pages 8-16
The Tamagawa Number and the Volume of G(?)/G(?)....Pages 17-30
The Size of Г....Pages 31-40
Margulis’ Finiteness Theorem....Pages 41-59
A Zariski Dense and a Free Subgroup of Г....Pages 60-65
An Example....Pages 66-71
Problems....Pages 72-76
Back Matter....Pages 77-80

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This book is devoted to a study of the unit groups of orders in skew fields, finite dimensional and central over the rational field; it thereby belongs to the field of noncommutative arithmetic. Its purpose is a synopsis of results and methods, including full proofs of the most important results. It is addressed to researchers in number theory and arithmetic groups.
Content:
Front Matter....Pages i-viii
Basic Facts....Pages 1-4
Hey’s Theorem and Consequences....Pages 5-7
Siegel-Weyl Reduction Theory....Pages 8-16
The Tamagawa Number and the Volume of G(?)/G(?)....Pages 17-30
The Size of Г....Pages 31-40
Margulis’ Finiteness Theorem....Pages 41-59
A Zariski Dense and a Free Subgroup of Г....Pages 60-65
An Example....Pages 66-71
Problems....Pages 72-76
Back Matter....Pages 77-80
....