Author: Paul Moritz CohnPublisher:
ISBN:
Category : Associative rings
Languages : en
Pages : 632
Book Description
Free Rings and Their Relations
Author: Paul Moritz CohnPublisher:
ISBN:
Category : Associative rings
Languages : en
Pages : 632
Book Description
Free Rings and Their Relations. Cohn
Author: Paul Moritz CohnFree rings & their relations ...
Author: CohnFree Ideal Rings and Localization in General Rings
Author: P. M. CohnPublisher: Cambridge University Press
ISBN: 1139454994
Category : Mathematics
Languages : en
Pages : 21
Book Description
Proving that a polynomial ring in one variable over a field is a principal ideal domain can be done by means of the Euclidean algorithm, but this does not extend to more variables. However, if the variables are not allowed to commute, giving a free associative algebra, then there is a generalization, the weak algorithm, which can be used to prove that all one-sided ideals are free. This book presents the theory of free ideal rings (firs) in detail. Particular emphasis is placed on rings with a weak algorithm, exemplified by free associative algebras. There is also a full account of localization which is treated for general rings but the features arising in firs are given special attention. Each section has a number of exercises, including some open problems, and each chapter ends in a historical note.
Rings, Modules and Representations
Author: Viet Dung NguyenPublisher: American Mathematical Soc.
ISBN: 0821843702
Category : Mathematics
Languages : en
Pages : 377
Book Description
The papers in this volume contain results in active research areas in the theory of rings and modules, including non commutative and commutative ring theory, module theory, representation theory, and coding theory.
Cogroups and Co-rings in Categories of Associative Rings
Author: George M. BergmanPublisher: American Mathematical Soc.
ISBN: 0821804952
Category : Mathematics
Languages : en
Pages : 400
Book Description
This book studies representable functors among well-known varieties of algebras. All such functors from associative rings over a fixed ring R to each of the categories of abelian groups, associative rings, Lie rings, and to several others are determined. Results are also obtained on representable functors on varieties of groups, semigroups, commutative rings, and Lie algebras. The book includes a "Symbol index", which serves as a glossary of symbols used and a list of the pages where the topics so symbolized are treated, and a "Word and phrase index". The authors have strived -- and succeeded -- in creating a volume that is very user-friendly.
Skew Fields
Author: Paul Moritz CohnPublisher: Cambridge University Press
ISBN: 0521432170
Category : Mathematics
Languages : en
Pages : 522
Book Description
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.
Ring Theory, Antwerp 1980
Author: F. van OystaeyenPublisher: Springer
ISBN: 3540383344
Category : Mathematics
Languages : en
Pages : 220
Book Description
Advances in Non-Commutative Ring Theory
Author: P. J. FleuryPublisher: Springer
ISBN: 3540393714
Category : Mathematics
Languages : en
Pages : 152
Book Description
Ring Theory - Proceedings Of The Biennial Ohio State-denison Conference 1992
Author: Surender K JainPublisher: World Scientific
ISBN: 9814553123
Category :
Languages : en
Pages : 394
Book Description
This volume consists of a collection of invited papers on the theory of rings and modules, most of which were presented at the biennial Ohio State — Denison Conference, May 1992, in memory of Hans Zassenhaus. The topics of these papers represent many modern trends in Ring Theory. The wide variety of methodologies and techniques demonstrated will be valuable in particular to young researchers in the area. Covering a broad range, this book should appeal to a wide spectrum of researchers in algebra and number theory.