Author : Ernst Kleinert
Publisher : Birkhäuser
Page : 89 pages
File Size : 38,9 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 3034884095
This book is devoted to a study of the unit groups of orders in skew fields, finite dimensional and central over the rational field; it thereby belongs to the field of noncommutative arithmetic. Its purpose is a synopsis of results and methods, including full proofs of the most important results. It is addressed to researchers in number theory and arithmetic groups.
Author : Paul Moritz Cohn
Publisher : Cambridge University Press
Page : 522 pages
File Size : 32,85 MB
Release : 1995-07-28
Category : Mathematics
ISBN : 0521432170
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.
Author : P. M. Cohn
Publisher : CUP Archive
Page : 276 pages
File Size : 31,71 MB
Release : 1977-04-28
Category : Mathematics
ISBN : 9780521214971
"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
Author : A. H. Schofield
Publisher : Cambridge University Press
Page : 237 pages
File Size : 50,38 MB
Release : 1985-04-18
Category : Mathematics
ISBN : 0521278538
A study of representations of rings over skew fields.
Author : Eric Jespers
Publisher : Walter de Gruyter GmbH & Co KG
Page : 228 pages
File Size : 36,41 MB
Release : 2015-11-13
Category : Mathematics
ISBN : 3110411504
This two-volume graduate textbook gives a comprehensive, state-of-the-art account of describing large subgroups of the unit group of the integral group ring of a finite group and, more generally, of the unit group of an order in a finite dimensional semisimple rational algebra. Since the book is addressed to graduate students as well as young researchers, all required background on these diverse areas, both old and new, is included. Supporting problems illustrate the results and complete some of the proofs. Volume 1 contains all the details on describing generic constructions of units and the subgroup they generate. Volume 2 mainly is about structure theorems and geometric methods. Without being encyclopaedic, all main results and techniques used to achieve these results are included. Basic courses in group theory, ring theory and field theory are assumed as background.
Author : Steven Howard Weintraub
Publisher : World Scientific
Page : 438 pages
File Size : 25,40 MB
Release : 2022-05-25
Category : Mathematics
ISBN : 9811246688
This book is a textbook for a semester-long or year-long introductory course in abstract algebra at the upper undergraduate or beginning graduate level.It treats set theory, group theory, ring and ideal theory, and field theory (including Galois theory), and culminates with a treatment of Dedekind rings, including rings of algebraic integers.In addition to treating standard topics, it contains material not often dealt with in books at this level. It provides a fresh perspective on the subjects it covers, with, in particular, distinctive treatments of factorization theory in integral domains and of Galois theory.As an introduction, it presupposes no prior knowledge of abstract algebra, but provides a well-motivated, clear, and rigorous treatment of the subject, illustrated by many examples. Written with an eye toward number theory, it contains numerous applications to number theory (including proofs of Fermat's theorem on sums of two squares and of the Law of Quadratic Reciprocity) and serves as an excellent basis for further study in algebra in general and number theory in particular.Each of its chapters concludes with a variety of exercises ranging from the straightforward to the challenging in order to reinforce students' knowledge of the subject. Some of these are particular examples that illustrate the theory while others are general results that develop the theory further.
Author : Library of Congress
Publisher :
Page : 1942 pages
File Size : 33,57 MB
Release : 2006
Category : Subject headings, Library of Congress
ISBN :
Author : Library of Congress. Cataloging Policy and Support Office
Publisher :
Page : 1938 pages
File Size : 16,25 MB
Release : 2006
Category : Subject headings, Library of Congress
ISBN :
Author :
Publisher :
Page : pages
File Size : 43,1 MB
Release : 2009
Category : Subject headings, Library of Congress
ISBN :
Author : Eberhard Zeidler
Publisher : Springer Science & Business Media
Page : 1125 pages
File Size : 24,41 MB
Release : 2008-09-03
Category : Mathematics
ISBN : 3540853774
And God said, Let there be light; and there was light. Genesis 1,3 Light is not only the basis of our biological existence, but also an essential source of our knowledge about the physical laws of nature, ranging from the seventeenth century geometrical optics up to the twentieth century theory of general relativity and quantum electrodynamics. Folklore Don’t give us numbers: give us insight! A contemporary natural scientist to a mathematician The present book is the second volume of a comprehensive introduction to themathematicalandphysicalaspectsofmodernquantum?eldtheorywhich comprehends the following six volumes: Volume I: Basics in Mathematics and Physics Volume II: Quantum Electrodynamics Volume III: Gauge Theory Volume IV: Quantum Mathematics Volume V: The Physics of the Standard Model Volume VI: Quantum Gravitation and String Theory. It is our goal to build a bridge between mathematicians and physicists based on the challenging question about the fundamental forces in • macrocosmos (the universe) and • microcosmos (the world of elementary particles). The six volumes address a broad audience of readers, including both und- graduate and graduate students, as well as experienced scientists who want to become familiar with quantum ?eld theory, which is a fascinating topic in modern mathematics and physics.
