Download or read book Skew Field Constructions written by P. M. Cohn and published by CUP Archive. This book was released on 1977-04-28 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: "These notes describe methods of constructing skew fields, in particular the coproduct coconstruction discovered by the author, and trace out some of the consequences using the powerful coproduct theorems of G.M. Bergman, which are proved here."- publisher
Download or read book Skew Fields written by Paul Moritz Cohn and published by Cambridge University Press. This book was released on 1995-07-28 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: Non-commutative fields (also called skew fields or division rings) have not been studied as thoroughly as their commutative counterparts and most accounts have hitherto been confined to division algebras, that is skew fields finite-dimensional over their centre. Based on the author's LMS lecture note volume Skew Field Constructions, the present work offers a comprehensive account of skew fields. The axiomatic foundation and a precise description of the embedding problem are followed by an account of algebraic and topological construction methods, in particular, the author's general embedding theory is presented with full proofs, leading to the construction of skew fields. The powerful coproduct theorems of G. M. Bergman are proved here as well as the properties of the matrix reduction functor, a useful but little-known construction providing a source of examples and counter-examples. The construction and basic properties of existentially closed skew fields are given, leading to an example of a model class with an infinite forcing companion which is not axiomatizable. The treatment of equations over skew fields has been simplified and extended by the use of matrix methods, and the beginnings of non-commutative algebraic geometry are presented, with a precise account of the problems that need to be overcome for a satisfactory theory. A separate chapter describes valuations and orderings on skew fields, with a construction applicable to free fields. Numerous exercises test the reader's understanding, presenting further aspects and open problems in concise form, and notes and comments at the ends of chapters provide historical background.
Download or read book Skew Fields written by P. K. Draxl and published by Cambridge University Press. This book was released on 1983-02-17 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is written in three parts. Part I consists of preparatory work on algebras, needed in Parts II and III. Part II consists of a modern description of the theory of Brauer groups over fields (from as elementary a point of view as possible). Part III covers some new developments in the theory which, until now, have not been available except in journals.
Download or read book Further Algebra and Applications written by Paul M. Cohn and published by Springer Science & Business Media. This book was released on 2011-06-27 with total page 454 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Representations of Rings Over Skew Fields written by A. H. Schofield and published by Cambridge University Press. This book was released on 1985-04-18 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: A study of representations of rings over skew fields.
Download or read book A Guide to Groups Rings and Fields written by Fernando Q. Gouvêa and published by MAA. This book was released on 2012 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: Insightful overview of many kinds of algebraic structures that are ubiquitous in mathematics. For researchers at graduate level and beyond.
Download or read book Lond Mathematical Society Lecture Note Series 81 Skew Fields written by and published by CUP Archive. This book was released on with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Valuations of Skew Fields and Projective Hjelmslev Spaces written by Karl Mathiak and published by Springer. This book was released on 2006-11-14 with total page 123 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Ring Constructions and Applications written by Andrei V. Kelarev and published by World Scientific. This book was released on 2002 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the definitions of several ring constructions used in various applications. The concept of a groupoid-graded ring includes many of these constructions as special cases and makes it possible to unify the exposition. Recent research results on groupoid-graded rings and more specialized constructions are presented. In addition, there is a chapter containing open problems currently considered in the literature. Ring Constructions and Applications can serve as an excellent introduction for graduate students to many ring constructions as well as to essential basic concepts of group, semigroup and ring theories used in proofs. Contents: Preliminaries; Graded Rings; Examples of Ring Constructions; The Jacobson Radical; Groups of Units; Finiteness Conditions; PI-Rings and Varieties; Gradings of Matrix Rings; Examples of Applications; Open Problems. Readership: Graduate students and researchers using ring constructions in their work.
Download or read book Encyclopaedia of Mathematics written by Michiel Hazewinkel and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 549 pages. Available in PDF, EPUB and Kindle. Book excerpt: This ENCYCLOPAEDIA OF MATHEMATICS aims to be a reference work for all parts of mathe matics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977-1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fine subdivi sion has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathematics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, en gineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques.
Download or read book The Classical Fields written by H. Salzmann and published by Cambridge University Press. This book was released on 2007-08-23 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: The real, rational, complex and p-adic numbers are discussed in detail in this comprehensive work.
Download or read book Advances in Algebra and Model Theory written by M Droste and published by CRC Press. This book was released on 1998-01-29 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains 25 surveys in algebra and model theory, all written by leading experts in the field. The surveys are based around talks given at conferences held in Essen, 1994, and Dresden, 1995. Each contribution is written in such a way as to highlight the ideas that were discussed at the conferences, and also to stimulate open research problems in a form accessible to the whole mathematical community. The topics include field and ring theory as well as groups, ordered algebraic structure and their relationship to model theory. Several papers deal with infinite permutation groups, abelian groups, modules and their relatives and representations. Model theoretic aspects include quantifier elimination in skew fields, Hilbert's 17th problem, (aleph-0)-categorical structures and Boolean algebras. Moreover symmetry questions and automorphism groups of orders are covered. This work contains 25 surveys in algebra and model theory, each is written in such a way as to highlight the ideas that were discussed at Conferences, and also to stimulate open research problems in a form accessible to the whole mathematical community.
Download or read book Hadamard Matrices written by Jennifer Seberry and published by John Wiley & Sons. This book was released on 2020-08-25 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: Up-to-date resource on Hadamard matrices Hadamard Matrices: Constructions using Number Theory and Algebra provides students with a discussion of the basic definitions used for Hadamard Matrices as well as more advanced topics in the subject, including: Gauss sums, Jacobi sums and relative Gauss sums Cyclotomic numbers Plug-in matrices, arrays, sequences and M-structure Galois rings and Menon Hadamard differences sets Paley difference sets and Paley type partial difference sets Symmetric Hadamard matrices, skew Hadamard matrices and amicable Hadamard matrices A discussion of asymptotic existence of Hadamard matrices Maximal determinant matrices, embeddability of Hadamard matrices and growth problem for Hadamard matrices The book can be used as a textbook for graduate courses in combinatorics, or as a reference for researchers studying Hadamard matrices. Utilized in the fields of signal processing and design experiments, Hadamard matrices have been used for 150 years, and remain practical today. Hadamard Matrices combines a thorough discussion of the basic concepts underlying the subject matter with more advanced applications that will be of interest to experts in the area.
Download or read book Introduction to Ring Theory written by Paul M. Cohn and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: A clear and structured introduction to the subject. After a chapter on the definition of rings and modules there are brief accounts of Artinian rings, commutative Noetherian rings and ring constructions, such as the direct product, Tensor product and rings of fractions, followed by a description of free rings. Readers are assumed to have a basic understanding of set theory, group theory and vector spaces. Over two hundred carefully selected exercises are included, most with outline solutions.
Download or read book Formal Power Series and Algebraic Combinatorics written by Daniel Krob and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 815 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the extended abstracts presented at the 12th International Conference on Power Series and Algebraic Combinatorics (FPSAC '00) that took place at Moscow State University, June 26-30, 2000. These proceedings cover the most recent trends in algebraic and bijective combinatorics, including classical combinatorics, combinatorial computer algebra, combinatorial identities, combinatorics of classical groups, Lie algebra and quantum groups, enumeration, symmetric functions, young tableaux etc...
Download or read book WORD PROBLEMS II written by Lev D. Beklemishev and published by Elsevier. This book was released on 2000-04-01 with total page 589 pages. Available in PDF, EPUB and Kindle. Book excerpt: WORD PROBLEMS II
Download or read book Rings and Geometry written by R. Kaya and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 567 pages. Available in PDF, EPUB and Kindle. Book excerpt: When looking for applications of ring theory in geometry, one first thinks of algebraic geometry, which sometimes may even be interpreted as the concrete side of commutative algebra. However, this highly de veloped branch of mathematics has been dealt with in a variety of mono graphs, so that - in spite of its technical complexity - it can be regarded as relatively well accessible. While in the last 120 years algebraic geometry has again and again attracted concentrated interes- which right now has reached a peak once more - , the numerous other applications of ring theory in geometry have not been assembled in a textbook and are scattered in many papers throughout the literature, which makes it hard for them to emerge from the shadow of the brilliant theory of algebraic geometry. It is the aim of these proceedings to give a unifying presentation of those geometrical applications of ring theo~y outside of algebraic geometry, and to show that they offer a considerable wealth of beauti ful ideas, too. Furthermore it becomes apparent that there are natural connections to many branches of modern mathematics, e. g. to the theory of (algebraic) groups and of Jordan algebras, and to combinatorics. To make these remarks more precise, we will now give a description of the contents. In the first chapter, an approach towards a theory of non-commutative algebraic geometry is attempted from two different points of view.
