The Multiplicative Semigroup of a Ring and the Embedding of Rings in Skew Fields
Author : A. J. Bowtell
Publisher :
Page : pages
File Size : 43,28 MB
Release : 1967
Category :
ISBN :
Author : A. J. Bowtell
Publisher :
Page : pages
File Size : 43,28 MB
Release : 1967
Category :
ISBN :
Author : John Jim Papadopoulos
Publisher :
Page : 52 pages
File Size : 30,3 MB
Release : 1974
Category :
ISBN :
Author : P. M. Cohn
Publisher : Cambridge University Press
Page : 21 pages
File Size : 18,4 MB
Release : 2006-06-08
Category : Mathematics
ISBN : 1139454994
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.
Author : A. G. Kurosh
Publisher : Elsevier
Page : 375 pages
File Size : 15,27 MB
Release : 2014-07-10
Category : Mathematics
ISBN : 1483149579
Lectures in General Algebra is a translation from the Russian and is based on lectures on specialized courses in general algebra at Moscow University. The book starts with the basics of algebra. The text briefly describes the theory of sets, binary relations, equivalence relations, partial ordering, minimum condition, and theorems equivalent to the axiom of choice. The text gives the definition of binary algebraic operation and the concepts of groups, groupoids, and semigroups. The book examines the parallelism between the theory of groups and the theory of rings; such examinations show the convenience of constructing a single theory from the results of group experiments and ring experiments which are known to follow simple corollaries. The text also presents algebraic structures that are not of binary nature. From this parallelism arise other concepts, such as that of the lattices, complete lattices, and modular lattices. The book then proves the Schmidt-Ore theorem, and also describes linear algebra, as well as the Birkhoff-Witt theorem on Lie algebras. The text also addresses ordered groups, the Archimedean groups and rings, and Albert's theorem on normed algebras. This book can prove useful for algebra students and for professors of algebra and advanced mathematicians.
Author : W. B. Vasantha Kandasamy
Publisher : Infinite Study
Page : 222 pages
File Size : 45,67 MB
Release : 2002
Category : Mathematics
ISBN : 1931233640
Generally, in any human field, a Smarandache Structure on a set A means a weak structure W on A such that there exists a proper subset B which is embedded with a stronger structure S.By proper subset one understands a set included in A, different from the empty set, from the unit element if any, and from A.These types of structures occur in our every day?s life, that?s why we study them in this book.Thus, as two particular cases:A Smarandache ring of level I (S-ring I) is a ring R that contains a proper subset that is a field with respect to the operations induced. A Smarandache ring of level II (S-ring II) is a ring R that contains a proper subset A that verifies: ?A is an additive abelian group; ?A is a semigroup under multiplication;?For a, b I A, a?b = 0 if and only if a = 0 or b = 0.
Author : G. Karpilovsky
Publisher : Elsevier
Page : 277 pages
File Size : 47,19 MB
Release : 2011-09-22
Category : Mathematics
ISBN : 0080872379
A broad range of topics is covered here, including commutative monoid rings, the Jacobson radical of semigroup rings, blocks of modular group algebras, nilpotency index of the radical of group algebras, the isomorphism problem for group rings, inverse semigroup algebras and the Picard group of an abelian group ring. The survey lectures provide an up-to-date account of the current state of the subject and form a comprehensive introduction for intending researchers.
Author : Robert Gilmer
Publisher : University of Chicago Press
Page : 392 pages
File Size : 49,8 MB
Release : 1984-03-15
Category : Mathematics
ISBN : 0226293920
Commutative Semigroup Rings was the first exposition of the basic properties of semigroup rings. Gilmer concentrates on the interplay between semigroups and rings, thereby illuminating both of these important concepts in modern algebra.
Author : Christopher Hollings
Publisher : American Mathematical Society
Page : 457 pages
File Size : 15,7 MB
Release : 2014-07-16
Category : Mathematics
ISBN : 1470414937
The theory of semigroups is a relatively young branch of mathematics, with most of the major results having appeared after the Second World War. This book describes the evolution of (algebraic) semigroup theory from its earliest origins to the establishment of a full-fledged theory. Semigroup theory might be termed `Cold War mathematics' because of the time during which it developed. There were thriving schools on both sides of the Iron Curtain, although the two sides were not always able to communicate with each other, or even gain access to the other's publications. A major theme of this book is the comparison of the approaches to the subject of mathematicians in East and West, and the study of the extent to which contact between the two sides was possible.
Author : A. H. Schofield
Publisher : Cambridge University Press
Page : 237 pages
File Size : 27,1 MB
Release : 1985-04-18
Category : Mathematics
ISBN : 0521278538
A study of representations of rings over skew fields.
Author : Lev D. Beklemishev
Publisher : Elsevier
Page : 589 pages
File Size : 50,92 MB
Release : 2000-04-01
Category : Computers
ISBN : 0080955037
WORD PROBLEMS II