The Level of Cyclic Division Algebras
Author | : M. Denert |
Publisher | : |
Total Pages | : 178 |
Release | : 198? |
Genre | : |
ISBN | : |
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Author | : M. Denert |
Publisher | : |
Total Pages | : 178 |
Release | : 198? |
Genre | : |
ISBN | : |
Author | : Frédérique Oggier |
Publisher | : |
Total Pages | : 0 |
Release | : 2007 |
Genre | : |
ISBN | : |
Author | : Paul M. Cohn |
Publisher | : Springer Science & Business Media |
Total Pages | : 454 |
Release | : 2011-06-27 |
Genre | : Mathematics |
ISBN | : 1447100395 |
Here is the second volume of a revised edition of P.M. Cohn's classic three-volume text Algebra, widely regarded as one of the most outstanding introductory algebra textbooks. Volume Two focuses on applications. The text is supported by worked examples, with full proofs, there are numerous exercises with occasional hints, and some historical remarks.
Author | : Albrecht Pfister |
Publisher | : Cambridge University Press |
Total Pages | : 191 |
Release | : 1995-09-28 |
Genre | : Mathematics |
ISBN | : 0521467551 |
A gem of a book bringing together 30 years worth of results that are certain to interest anyone whose research touches on quadratic forms.
Author | : Jean-Pierre Tignol |
Publisher | : Springer |
Total Pages | : 652 |
Release | : 2015-04-03 |
Genre | : Mathematics |
ISBN | : 3319163604 |
This monograph is the first book-length treatment of valuation theory on finite-dimensional division algebras, a subject of active and substantial research over the last forty years. Its development was spurred in the last decades of the twentieth century by important advances such as Amitsur's construction of non crossed products and Platonov's solution of the Tannaka-Artin problem. This study is particularly timely because it approaches the subject from the perspective of associated graded structures. This new approach has been developed by the authors in the last few years and has significantly clarified the theory. Various constructions of division algebras are obtained as applications of the theory, such as noncrossed products and indecomposable algebras. In addition, the use of valuation theory in reduced Whitehead group calculations (after Hazrat and Wadsworth) and in essential dimension computations (after Baek and Merkurjev) is showcased. The intended audience consists of graduate students and research mathematicians.
Author | : Abraham Adrian Albert |
Publisher | : American Mathematical Soc. |
Total Pages | : 224 |
Release | : 1939-12-31 |
Genre | : Mathematics |
ISBN | : 0821810243 |
The first three chapters of this work contain an exposition of the Wedderburn structure theorems. Chapter IV contains the theory of the commutator subalgebra of a simple subalgebra of a normal simple algebra, the study of automorphisms of a simple algebra, splitting fields, and the index reduction factor theory. The fifth chapter contains the foundation of the theory of crossed products and of their special case, cyclic algebras. The theory of exponents is derived there as well as the consequent factorization of normal division algebras into direct factors of prime-power degree. Chapter VI consists of the study of the abelian group of cyclic systems which is applied in Chapter VII to yield the theory of the structure of direct products of cyclic algebras and the consequent properties of norms in cyclic fields. This chapter is closed with the theory of $p$-algebras. In Chapter VIII an exposition is given of the theory of the representations of algebras. The treatment is somewhat novel in that while the recent expositions have used representation theorems to obtain a number of results on algebras, here the theorems on algebras are themselves used in the derivation of results on representations. The presentation has its inspiration in the author's work on the theory of Riemann matrices and is concluded by the introduction to the generalization (by H. Weyl and the author) of that theory. The theory of involutorial simple algebras is derived in Chapter X both for algebras over general fields and over the rational field. The results are also applied in the determination of the structure of the multiplication algebras of all generalized Riemann matrices, a result which is seen in Chapter XI to imply a complete solution of the principal problem on Riemann matrices.
Author | : David J. Saltman |
Publisher | : American Mathematical Soc. |
Total Pages | : 132 |
Release | : |
Genre | : Mathematics |
ISBN | : 9780821889381 |
This volume is based on lectures on division algebras given at a conference held at Colorado State University. Although division algebras are a very classical object, this book presents this "classical" material in a new way, highlighting current approaches and new theorems, and illuminating the connections with a variety of areas in mathematics.
Author | : |
Publisher | : |
Total Pages | : 418 |
Release | : 1997 |
Genre | : Mathematics |
ISBN | : |
Author | : Bharath Al Sethuraman |
Publisher | : |
Total Pages | : 170 |
Release | : 1991 |
Genre | : |
ISBN | : |
Author | : Franz-Viktor Kuhlmann |
Publisher | : American Mathematical Soc. |
Total Pages | : 470 |
Release | : 2002-01-01 |
Genre | : Mathematics |
ISBN | : 9780821871393 |
This book is the first of two proceedings volumes stemming from the International Conference and Workshop on Valuation Theory held at the University of Saskatchewan (Saskatoon, SK, Canada). Valuation theory arose in the early part of the twentieth century in connection with number theory and has many important applications to geometry and analysis: the classical application to the study of algebraic curves and to Dedekind and Prufer domains; the close connection to the famousresolution of the singularities problem; the study of the absolute Galois group of a field; the connection between ordering, valuations, and quadratic forms over a formally real field; the application to real algebraic geometry; the study of noncommutative rings; etc. The special feature of this book isits focus on current applications of valuation theory to this broad range of topics. Also included is a paper on the history of valuation theory. The book is suitable for graduate students and research mathematicians working in algebra, algebraic geometry, number theory, and mathematical logic.