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| Author | : Tsit-Yuen Lam |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 158 |
| Release | : 1983 |
| Genre | : Mathematics |
| ISBN | : 0821807021 |
Presents an introduction to ordered fields and reduced quadratic forms using valuation-theoretic techniques. This book describes the techniques of residue forms and the relevant Springer theory.
| Author | : Tsit-Yuen Lam |
| Publisher | : |
| Total Pages | : 143 |
| Release | : 1970 |
| Genre | : Forms, Quadratic |
| ISBN | : 9780821807026 |
| Author | : Murray A. Marshall |
| Publisher | : Springer |
| Total Pages | : 198 |
| Release | : 2014-10-08 |
| Genre | : Mathematics |
| ISBN | : 9783662204276 |
This book is of interest to students as well as experts in the area of real algebraic geometry, quadratic forms, orderings, valuations, lattice ordered groups and rings, and in model theory. The original motivation comes from orderings on fields and commutative rings. This is explained as is the important application to minimal generation of semi-algebraic sets. Many results in the new theory of abstract real spectra (also called spaces of signs) appear here for the first time. The reader needs elementary knowledge of commutative rings, ordered fields and real closed fields and valuations.
| 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.
| Author | : McMaster University |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 362 |
| Release | : 1984 |
| Genre | : Mathematics |
| ISBN | : 9780821860083 |
Contains the proceedings of the 1983 Seminar on Quadratic and Hermitian Forms held at McMaster University, July 1983. Between 1945 and 1965, most of the work in quadratic (and hermitian) forms took place in arithmetic theory (M Eichler, M Kneser, O T O'Meara).
| Author | : Eva Bayer-Fluckiger |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 330 |
| Release | : 2000 |
| Genre | : Mathematics |
| ISBN | : 0821827790 |
This volume outlines the proceedings of the conference on "Quadratic Forms and Their Applications" held at University College Dublin. It includes survey articles and research papers ranging from applications in topology and geometry to the algebraic theory of quadratic forms and its history. Various aspects of the use of quadratic forms in algebra, analysis, topology, geometry, and number theory are addressed. Special features include the first published proof of the Conway-Schneeberger Fifteen Theorem on integer-valued quadratic forms and the first English-language biography of Ernst Witt, founder of the theory of quadratic forms.
| Author | : Murray Marshall |
| Publisher | : New York : Springer |
| Total Pages | : 206 |
| Release | : 1996-10-02 |
| Genre | : Mathematics |
| ISBN | : |
This book is of interest to students as well as experts in the area of real algebraic geometry, quadratic forms, orderings, valuations, lattice ordered groups and rings, and in model theory. The original motivation comes from orderings on fields and commutative rings. This is explained as is the important application to minimal generation of semi-algebraic sets. Many results in the new theory of abstract real spectra (also called spaces of signs) appear here for the first time. The reader needs elementary knowledge of commutative rings, ordered fields and real closed fields and valuations.
| Author | : T.Y. Lam |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 578 |
| Release | : |
| Genre | : Forms, Quadratic |
| ISBN | : 9780821872413 |
This new version of the author's prizewinning book, Algebraic Theory of Quadratic Forms (W. A. Benjamin, Inc., 1973), gives a modern and self-contained introduction to the theory of quadratic forms over fields of characteristic different from two. Starting with few prerequisites beyond linear algebra, the author charts an expert course from Witt's classical theory of quadratic forms, quaternion and Clifford algebras, Artin-Schreier theory of formally real fields, and structural theorems on Witt rings, to the theory of Pfister forms, function fields, and field invariants. These main developments are seamlessly interwoven with excursions into Brauer-Wall groups, local and global fields, trace forms, Galois theory, and elementary algebraic K-theory, to create a uniquely original treatment of quadratic form theory over fields. Two new chapters totaling more than 100 pages have been added to the earlier incarnation of this book to take into account some of the newer results and more recent viewpoints in the area. As is characteristic of this author's expository style, the presentation of the main material in this book is interspersed with a copious number of carefully chosen examples to illustrate the general theory. This feature, together with a rich stock of some 280 exercises for the thirteen chapters, greatly enhances the pedagogical value of this book, both as a graduate text and as a reference work for researchers in algebra, number theory, algebraic geometry, algebraic topology, and geometric topology.
| Author | : J. W. S. Cassels |
| Publisher | : Courier Dover Publications |
| Total Pages | : 429 |
| Release | : 2008-08-08 |
| Genre | : Mathematics |
| ISBN | : 0486466701 |
Exploration of quadratic forms over rational numbers and rational integers offers elementary introduction. Covers quadratic forms over local fields, forms with integral coefficients, reduction theory for definite forms, more. 1968 edition.
| Author | : M. Hazewinkel |
| Publisher | : Elsevier |
| Total Pages | : 637 |
| Release | : 2009-07-08 |
| Genre | : Mathematics |
| ISBN | : 0080932819 |
Algebra, as we know it today, consists of many different ideas, concepts and results. A reasonable estimate of the number of these different items would be somewhere between 50,000 and 200,000. Many of these have been named and many more could (and perhaps should) have a name or a convenient designation. Even the nonspecialist is likely to encounter most of these, either somewhere in the literature, disguised as a definition or a theorem or to hear about them and feel the need for more information. If this happens, one should be able to find enough information in this Handbook to judge if it is worthwhile to pursue the quest. In addition to the primary information given in the Handbook, there are references to relevant articles, books or lecture notes to help the reader. An excellent index has been included which is extensive and not limited to definitions, theorems etc. The Handbook of Algebra will publish articles as they are received and thus the reader will find in this third volume articles from twelve different sections. The advantages of this scheme are two-fold: accepted articles will be published quickly and the outline of the Handbook can be allowed to evolve as the various volumes are published. A particularly important function of the Handbook is to provide professional mathematicians working in an area other than their own with sufficient information on the topic in question if and when it is needed. - Thorough and practical source of information - Provides in-depth coverage of new topics in algebra - Includes references to relevant articles, books and lecture notes
