## Lectures on Division Algebras

Author: David J. Saltman

Publisher: American Mathematical Soc.

ISBN: 0821809792

Category: Mathematics

Page: 120

View: 1969

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.
Release

## Valuation Theory and Its Applications

Author: Franz-Viktor Kuhlmann,Salma Kuhlmann,Murray Marshall

Publisher: American Mathematical Soc.

ISBN: 9780821871393

Category: Mathematics

Page: 449

View: 429

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.
Release

## Separable Algebras

Author: Timothy J. Ford

Publisher: American Mathematical Soc.

ISBN: 1470437708

Category: Associative rings

Page: 637

View: 2971

This book presents a comprehensive introduction to the theory of separable algebras over commutative rings. After a thorough introduction to the general theory, the fundamental roles played by separable algebras are explored. For example, Azumaya algebras, the henselization of local rings, and Galois theory are rigorously introduced and treated. Interwoven throughout these applications is the important notion of étale algebras. Essential connections are drawn between the theory of separable algebras and Morita theory, the theory of faithfully flat descent, cohomology, derivations, differentials, reflexive lattices, maximal orders, and class groups. The text is accessible to graduate students who have finished a first course in algebra, and it includes necessary foundational material, useful exercises, and many nontrivial examples.
Release

## Value Functions on Simple Algebras, and Associated Graded Rings

Publisher: Springer

ISBN: 3319163604

Category: Mathematics

Page: 643

View: 8134

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.
Release

Noncommutative View

Author: Louis Halle Rowen

Publisher: American Mathematical Soc.

ISBN: 082184153X

Category: Mathematics

Page: 648

View: 4683

This book is a companion volume to Graduate Algebra: Commutative View (published as volume 73 in this series). The main and most important feature of the book is that it presents a unified approach to many important topics, such as group theory, ring theory, Lie algebras, and gives conceptual proofs of many basic results of noncommutative algebra. There are also a number of major results in noncommutative algebra that are usually found only in technical works, such as Zelmanov's proof of the restricted Burnside problem in group theory, word problems in groups, Tits's alternative in algebraic groups, PI algebras, and many of the roles that Coxeter diagrams play in algebra. The first half of the book can serve as a one-semester course on noncommutative algebra, whereas the remaining part of the book describes some of the major directions of research in the past 100 years. The main text is extended through several appendices, which permits the inclusion of more advanced material, and numerous exercises. The only prerequisite for using the book is an undergraduate course in algebra; whenever necessary, results are quoted from Graduate Algebra: Commutative View.
Release

## Lectures on Division Algebras

Author: David J. Saltman

Publisher: American Mathematical Soc.

ISBN: 0821809792

Category: Mathematics

Page: 120

View: 1002

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.
Release

## Mathematical Reviews

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 3293

Release

## Pacific Journal of Mathematics

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 4176

Release

## The Polynomial Identities and Invariants of $n \times n$ Matrices

Author: Edward Formanek

Publisher: American Mathematical Soc.

ISBN: 0821807307

Category: Mathematics

Page: 57

View: 2707

The theory of polynomial identities, as a well-defined field of study, began with a well-known 1948 article of Kaplansky. The field since developed along two branches: the structural, which investigates the properties of rings that satisfy a polynomial identity; and the varietal, which investigates the set of polynomials in the free ring that vanish under all specializations in a given ring. This book is based on lectures delivered during an NSF-CBMS Regional Conference, held at DePaul University in July 1990, at which the author was the principal lecturer. The first part of the book is concerned with polynomial identity rings. The emphasis is on those parts of the theory related to $n\times n$ matrices, including the major structure theorems and the construction of certain polynomial identities and central polynomials for $n\times n$ matrices. The ring of generic matrices and its center is described. The author then moves on to the invariants of $n\times n$ matrices, beginning with the first and second fundamental theorems, which are used to describe the polynomial identities satisfied by $n\times n$ matrices. One of the exceptional features of this book is the way it emphasizes the connection between polynomial identities and invariants of $n\times n$ matrices. Accessible to those with background at the level of a first-year graduate course in algebra, this book gives readers an understanding of polynomial identity rings and invariant theory, as well as an indication of problems and research in these areas.
Release

## BPR

Author: N.A

Publisher: N.A

ISBN: N.A

Category: American literature

Page: N.A

View: 5617