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Author : Thomas Curtis Craven
Publisher :
ISBN 13 :
Total Pages : 160 pages
Book Rating : 4.E/5 ( download)
Download or read book Witt Rings and Ordering of Fields written by Thomas Curtis Craven and published by . This book was released on 1973 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : P.M. Cohn
Publisher : Springer Science & Business Media
ISBN 13 : 0857294288
Total Pages : 470 pages
Book Rating : 4.8/5 (572 download)
Download or read book Basic Algebra written by P.M. Cohn and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first 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. This volume covers the important results of algebra. Readers should have some knowledge of linear algebra, groups and fields, although all the essential facts and definitions are recalled.
Author : M. Hazewinkel
Publisher : Elsevier
ISBN 13 : 0080932819
Total Pages : 637 pages
Book Rating : 4.0/5 (89 download)
Download or read book Handbook of Algebra written by M. Hazewinkel and published by Elsevier. This book was released on 2009-07-08 with total page 637 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Author : Kazimierz Szymiczek
Publisher : CRC Press
ISBN 13 : 9789056990763
Total Pages : 508 pages
Book Rating : 4.9/5 (97 download)
Download or read book Bilinear Algebra written by Kazimierz Szymiczek and published by CRC Press. This book was released on 1997-09-05 with total page 508 pages. Available in PDF, EPUB and Kindle. Book excerpt: Giving an easily accessible elementary introduction to the algebraic theory of quadratic forms, this book covers both Witt's theory and Pfister's theory of quadratic forms. Leading topics include the geometry of bilinear spaces, classification of bilinear spaces up to isometry depending on the ground field, formally real fields, Pfister forms, the Witt ring of an arbitrary field (characteristic two included), prime ideals of the Witt ring, Brauer group of a field, Hasse and Witt invariants of quadratic forms, and equivalence of fields with respect to quadratic forms. Problem sections are included at the end of each chapter. There are two appendices: the first gives a treatment of Hasse and Witt invariants in the language of Steinberg symbols, and the second contains some more advanced problems in 10 groups, including the u-invariant, reduced and stable Witt rings, and Witt equivalence of fields.
Author : René Schoof
Publisher : Springer Science & Business Media
ISBN 13 : 1848001851
Total Pages : 125 pages
Book Rating : 4.8/5 (48 download)
Download or read book Catalan's Conjecture written by René Schoof and published by Springer Science & Business Media. This book was released on 2010-07-08 with total page 125 pages. Available in PDF, EPUB and Kindle. Book excerpt: Eugène Charles Catalan made his famous conjecture – that 8 and 9 are the only two consecutive perfect powers of natural numbers – in 1844 in a letter to the editor of Crelle’s mathematical journal. One hundred and fifty-eight years later, Preda Mihailescu proved it. Catalan’s Conjecture presents this spectacular result in a way that is accessible to the advanced undergraduate. The author dissects both Mihailescu’s proof and the earlier work it made use of, taking great care to select streamlined and transparent versions of the arguments and to keep the text self-contained. Only in the proof of Thaine’s theorem is a little class field theory used; it is hoped that this application will motivate the interested reader to study the theory further. Beautifully clear and concise, this book will appeal not only to specialists in number theory but to anyone interested in seeing the application of the ideas of algebraic number theory to a famous mathematical problem.
Author : Tsit-Yuen Lam
Publisher : American Mathematical Soc.
ISBN 13 : 0821810952
Total Pages : 577 pages
Book Rating : 4.8/5 (218 download)
Download or read book Introduction to Quadratic Forms over Fields written by Tsit-Yuen Lam and published by American Mathematical Soc.. This book was released on 2005 with total page 577 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Bill Jacob
Publisher : American Mathematical Soc.
ISBN 13 : 0821803409
Total Pages : 458 pages
Book Rating : 4.8/5 (218 download)
Download or read book $K$-Theory and Algebraic Geometry: Connections with Quadratic Forms and Division Algebras written by Bill Jacob and published by American Mathematical Soc.. This book was released on 1995 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: Volume 2 of two - also available in a set of both volumes.
Author : Tsit-Yuen Lam
Publisher : Addison-Wesley
ISBN 13 : 9780805356663
Total Pages : 344 pages
Book Rating : 4.3/5 (566 download)
Download or read book The Algebraic Theory of Quadratic Forms written by Tsit-Yuen Lam and published by Addison-Wesley. This book was released on 1980 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Gregory W. Brumfiel
Publisher : Cambridge University Press
ISBN 13 : 052122845X
Total Pages : 293 pages
Book Rating : 4.5/5 (212 download)
Download or read book Partially Ordered Rings and Semi-Algebraic Geometry written by Gregory W. Brumfiel and published by Cambridge University Press. This book was released on 1979-12-20 with total page 293 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this unique book is to establish purely algebraic foundations for the development of certain parts of topology. Some topologists seek to understand geometric properties of solutions to finite systems of equations or inequalities and configurations which in some sense actually occur in the real world. Others study spaces constructed more abstractly using infinite limit processes. Their goal is to determine just how similar or different these abstract spaces are from those which are finitely described. However, as topology is usually taught, even the first, more concrete type of problem is approached using the language and methods of the second type. Professor Brumfiel's thesis is that this is unnecessary and, in fact, misleading philosophically. He develops a type of algebra, partially ordered rings, in which it makes sense to talk about solutions of equations and inequalities and to compare geometrically the resulting spaces. The importance of this approach is primarily that it clarifies the sort of geometrical questions one wants to ask and answer about those spaces which might have physical significance.
Author : Fabrizio Broglia
Publisher : American Mathematical Soc.
ISBN 13 : 1470429667
Total Pages : 390 pages
Book Rating : 4.4/5 (74 download)
Download or read book Ordered Algebraic Structures and Related Topics written by Fabrizio Broglia and published by American Mathematical Soc.. This book was released on 2017 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains the proceedings of the international conference "Ordered Algebraic Structures and Related Topics", held in October 2015, at CIRM, Luminy, Marseilles. Papers cover topics in real analytic geometry, real algebra, and real algebraic geometry including complexity issues, model theory of various algebraic and differential structures, Witt equivalence of fields, and the moment problem.
Author : Alexander V. Mikhalev
Publisher : Springer Science & Business Media
ISBN 13 : 9401732671
Total Pages : 629 pages
Book Rating : 4.4/5 (17 download)
Download or read book The Concise Handbook of Algebra written by Alexander V. Mikhalev and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 629 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is by no means clear what comprises the "heart" or "core" of algebra, the part of algebra which every algebraist should know. Hence we feel that a book on "our heart" might be useful. We have tried to catch this heart in a collection of about 150 short sections, written by leading algebraists in these areas. These sections are organized in 9 chapters A, B, . . . , I. Of course, the selection is partly based on personal preferences, and we ask you for your understanding if some selections do not meet your taste (for unknown reasons, we only had problems in the chapter "Groups" to get enough articles in time). We hope that this book sets up a standard of what all algebraists are supposed to know in "their" chapters; interested people from other areas should be able to get a quick idea about the area. So the target group consists of anyone interested in algebra, from graduate students to established researchers, including those who want to obtain a quick overview or a better understanding of our selected topics. The prerequisites are something like the contents of standard textbooks on higher algebra. This book should also enable the reader to read the "big" Handbook (Hazewinkel 1999-) and other handbooks. In case of multiple authors, the authors are listed alphabetically; so their order has nothing to do with the amounts of their contributions.
Author : Martin Aigner
Publisher : Springer Science & Business Media
ISBN 13 : 3662223430
Total Pages : 194 pages
Book Rating : 4.6/5 (622 download)
Download or read book Proofs from THE BOOK written by Martin Aigner and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: According to the great mathematician Paul Erdös, God maintains perfect mathematical proofs in The Book. This book presents the authors candidates for such "perfect proofs," those which contain brilliant ideas, clever connections, and wonderful observations, bringing new insight and surprising perspectives to problems from number theory, geometry, analysis, combinatorics, and graph theory. As a result, this book will be fun reading for anyone with an interest in mathematics.
Author : Richard S. Elman
Publisher : American Mathematical Soc.
ISBN 13 : 9780821873229
Total Pages : 456 pages
Book Rating : 4.8/5 (732 download)
Download or read book The Algebraic and Geometric Theory of Quadratic Forms written by Richard S. Elman and published by American Mathematical Soc.. This book was released on 2008-07-15 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a comprehensive study of the algebraic theory of quadratic forms, from classical theory to recent developments, including results and proofs that have never been published. The book is written from the viewpoint of algebraic geometry and includes the theory of quadratic forms over fields of characteristic two, with proofs that are characteristic independent whenever possible. For some results both classical and geometric proofs are given. Part I includes classical algebraic theory of quadratic and bilinear forms and answers many questions that have been raised in the early stages of the development of the theory. Assuming only a basic course in algebraic geometry, Part II presents the necessary additional topics from algebraic geometry including the theory of Chow groups, Chow motives, and Steenrod operations. These topics are used in Part III to develop a modern geometric theory of quadratic forms.
Download or read book Canadian Journal of Mathematics written by and published by . This book was released on 1983-06 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Kazimierz Szymiczek
Publisher : Routledge
ISBN 13 : 1351464205
Total Pages : 508 pages
Book Rating : 4.3/5 (514 download)
Download or read book Bilinear Algebra written by Kazimierz Szymiczek and published by Routledge. This book was released on 2017-11-22 with total page 508 pages. Available in PDF, EPUB and Kindle. Book excerpt: Giving an easily accessible elementary introduction to the algebraic theory of quadratic forms, this book covers both Witt's theory and Pfister's theory of quadratic forms. Leading topics include the geometry of bilinear spaces, classification of bilinear spaces up to isometry depending on the ground field, formally real fields, Pfister forms, the Witt ring of an arbitrary field (characteristic two included), prime ideals of the Witt ring, Brauer group of a field, Hasse and Witt invariants of quadratic forms, and equivalence of fields with respect to quadratic forms. Problem sections are included at the end of each chapter. There are two appendices: the first gives a treatment of Hasse and Witt invariants in the language of Steinberg symbols, and the second contains some more advanced problems in 10 groups, including the u-invariant, reduced and stable Witt rings, and Witt equivalence of fields.
Download or read book Canadian Journal of Mathematics written by and published by . This book was released on 1995-12 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Murray A. Marshall
Publisher : Springer
ISBN 13 : 3540699961
Total Pages : 191 pages
Book Rating : 4.5/5 (46 download)
Download or read book Spaces of Orderings and Abstract Real Spectra written by Murray A. Marshall and published by Springer. This book was released on 2006-11-17 with total page 191 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
