Valuation Theory and Its Applications

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

Publisher: American Mathematical Soc.

ISBN: 9780821871393

Category: Mathematics

Page: 449

View: 9359

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.

Value Functions on Simple Algebras, and Associated Graded Rings

Author: Jean-Pierre Tignol,Adrian R. Wadsworth

Publisher: Springer

ISBN: 3319163604

Category: Mathematics

Page: 643

View: 1017

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.

Graduate Algebra

Noncommutative View

Author: Louis Halle Rowen

Publisher: American Mathematical Soc.

ISBN: 082184153X

Category: Mathematics

Page: 648

View: 3022

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.

Quadratic Forms, Linear Algebraic Groups, and Cohomology

Author: Skip Garibaldi,R. Sujatha,Venapally Suresh

Publisher: Springer Science & Business Media

ISBN: 9781441962119

Category: Mathematics

Page: 348

View: 8097

The invited papers collected in this volume address topics related to the research of Raman Parimala (plenary speaker at the upcoming ICM 2010). These themes focus primarily on the interplay between algebra, number theory, and algebraic geometry. The included contributions cover exciting research in areas such as field patching and a proof of the Serre's Conjecture II for function fields of complex surfaces.

Lectures on Division Algebras

Author: David J. Saltman

Publisher: American Mathematical Soc.

ISBN: 0821809792

Category: Mathematics

Page: 120

View: 6578

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.

Lectures on Division Algebras

Author: David J. Saltman

Publisher: American Mathematical Soc.

ISBN: 0821809792

Category: Mathematics

Page: 120

View: 5125

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.

The Polynomial Identities and Invariants of N X N Matrices

Author: Edward Formanek

Publisher: American Mathematical Soc.

ISBN: 9780821889220

Category: Mathematics

Page: 57

View: 5928

The theory of polynomial identities, as a well-defined field of study, began with a well-known 1948 article of Kaplansky. The field has since developed along two branches: the structural, which investigates the properties of rings which satisfy a polynomial identity; and the varietal, which investigates the set of polynomials in the free ring which 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 x n matrices, including the major structure theorems and the construction of certain polynomials identities and central polynomials for n x n matrices. The ring of generic matrices and its centre is described. The author then moves on to the invariants of n x n matrices, beginning with the first and second fundamental theorems, which are used to describe the polynomial identities satisfied by n x n matrices. One of the exceptional features of this book is the way it emphasizes the connection between polynomial identities and invariants of n x 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 current problems and research in these areas.

Automorphic forms, automorphic representations, and arithmetic

NSF-CBMS Regional Conference in Mathematics on Euler Products and Eisenstein Series, May 20-24, 1996, Texas Christian University

Author: Robert S. Doran,Ze Li Dou,George T. Gilbert

Publisher: Amer Mathematical Society

ISBN: N.A

Category: Mathematics

Page: 608

View: 4671

Professor Goro Shimura was principal speaker at the conference on "Euler Products and Eisenstein Series" held at Texas Christian University (See CBMS Regional Conference Series in Mathematics, Volume 93). The present volume contains articles by leading specialists in the field. Some of these articles are based on talks given at the conference, whereas others were written purposely for this volume. The variety of the work presented reflects the current active state of thetopic.

American Book Publishing Record Cumulative, 1970-1974

Author: Bowker Editorial Staff

Publisher: N.A

ISBN: 9780835209113

Category:

Page: 6500

View: 6037

Here's quick access to more than 490,000 titles published from 1970 to 1984 arranged in Dewey sequence with sections for Adult and Juvenile Fiction. Author and Title indexes are included, and a Subject Guide correlates primary subjects with Dewey and LC classification numbers. These cumulative records are available in three separate sets.

Associations' Publications in Print

Author: N.A

Publisher: N.A

ISBN: 9780835214926

Category: Associations, institutions, etc

Page: N.A

View: 6950

1981- in 2 v.: v.1, Subject index; v.2, Title index, Publisher/title index, Association name index, Acronym index, Key to publishers' and distributors' abbreviations.

National Union Catalog

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Union catalogs

Page: N.A

View: 7933

Includes entries for maps and atlases.