Dimensions of Ring Theory

Dimensions of Ring Theory
Author: C. Nastasescu
Publisher: Springer Science & Business Media
Total Pages: 369
Release: 2012-12-06
Genre: Mathematics
ISBN: 9400938357

Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Gad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of s9phistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.

Advances in Ring Theory

Advances in Ring Theory
Author: S.K. Jain
Publisher: Springer Science & Business Media
Total Pages: 330
Release: 2012-12-06
Genre: Mathematics
ISBN: 1461219787

Introduction to Ring Theory

Introduction to Ring Theory
Author: Paul M. Cohn
Publisher: Springer Science & Business Media
Total Pages: 234
Release: 2012-12-06
Genre: Mathematics
ISBN: 1447104757

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.

Ring Theory, 83

Ring Theory, 83
Author: Louis H. Rowen
Publisher: Academic Press
Total Pages: 653
Release: 2012-12-02
Genre: Mathematics
ISBN: 0080925480

This is an abridged edition of the author's previous two-volume work, Ring Theory, which concentrates on essential material for a general ring theory course while ommitting much of the material intended for ring theory specialists. It has been praised by reviewers:**"As a textbook for graduate students, Ring Theory joins the best....The experts will find several attractive and pleasant features in Ring Theory. The most noteworthy is the inclusion, usually in supplements and appendices, of many useful constructions which are hard to locate outside of the original sources....The audience of nonexperts, mathematicians whose speciality is not ring theory, will find Ring Theory ideally suited to their needs....They, as well as students, will be well served by the many examples of rings and the glossary of major results."**--NOTICES OF THE AMS

Fields and Rings

Fields and Rings
Author: Irving Kaplansky
Publisher: University of Chicago Press
Total Pages: 217
Release: 1972
Genre: Mathematics
ISBN: 0226424510

This book combines in one volume Irving Kaplansky's lecture notes on the theory of fields, ring theory, and homological dimensions of rings and modules. "In all three parts of this book the author lives up to his reputation as a first-rate mathematical stylist. Throughout the work the clarity and precision of the presentation is not only a source of constant pleasure but will enable the neophyte to master the material here presented with dispatch and ease."—A. Rosenberg, Mathematical Reviews

Methods in Ring Theory

Methods in Ring Theory
Author: Freddy Van Oystaeyen
Publisher: Springer Science & Business Media
Total Pages: 569
Release: 2012-12-06
Genre: Mathematics
ISBN: 9400963696

Proceedings of the NATO Advanced Study Institute, Antwerp, Belgium, August 2-12, 1983

International Symposium on Ring Theory

International Symposium on Ring Theory
Author: Gary F. Birkenmeier
Publisher: Springer Science & Business Media
Total Pages: 468
Release: 2001
Genre: Mathematics
ISBN: 9780817641580

Ring theory provides the algebraic underpinnings for many areas of mathematics, computer science, and physics. For example, ring theory appears in: functional analysis; algebraic topology; algebraic number theory; coding theory; and in the study of quantum theory. This volume is a collection of research papers, many presented at the 3rd Korea-China-Japan International Symposium on Ring Theory held jointly with the 2nd Korea-Japan Ring Theory Seminar, in Korea, The articles examine wide-ranging developments and methodologies in various areas, including classical Hopf algebras and quantum groups.

A Course in Ring Theory

A Course in Ring Theory
Author: Donald S. Passman
Publisher: American Mathematical Soc.
Total Pages: 324
Release: 2004-09-28
Genre: Mathematics
ISBN: 9780821869383

Projective modules: Modules and homomorphisms Projective modules Completely reducible modules Wedderburn rings Artinian rings Hereditary rings Dedekind domains Projective dimension Tensor products Local rings Polynomial rings: Skew polynomial rings Grothendieck groups Graded rings and modules Induced modules Syzygy theorem Patching theorem Serre conjecture Big projectives Generic flatness Nullstellensatz Injective modules: Injective modules Injective dimension Essential extensions Maximal ring of quotients Classical ring of quotients Goldie rings Uniform dimension Uniform injective modules Reduced rank Index

Some Aspects of Ring Theory

Some Aspects of Ring Theory
Author: I. N. Herstein
Publisher: Springer Science & Business Media
Total Pages: 252
Release: 2011-06-01
Genre: Mathematics
ISBN: 3642110363

S. Amitsur: Associative rings with identities.- I.N. Herstein: Topics in ring theory.- N. Jacobson: Representation theory of Jordan algebras.- I. Kaplansky: The theory of homological dimension.- D. Buchsbaum: Complexes in local ring theory.- P.H. Cohn: Two topics in ring theory.- A.W. Goldie: Non-commutative localisation.