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.

Theory of Generalized Inverses Over Commutative Rings

Theory of Generalized Inverses Over Commutative Rings
Author: K.P.S. Bhaskara Rao
Publisher: CRC Press
Total Pages: 192
Release: 2002-03-21
Genre: Mathematics
ISBN: 0203218876

The theory of generalized inverses of real or complex matrices has been expertly developed and documented. But the generalized inverses of matrices over rings have received comprehensive treatment only recently. In this book, the author, who contributed to the research and development of the theory, explains his results. He explores regular element

Perspectives in Ring Theory

Perspectives in Ring Theory
Author: Freddy Van Oystaeyen
Publisher: Springer Science & Business Media
Total Pages: 386
Release: 2012-12-06
Genre: Mathematics
ISBN: 9400929854

This proceedings is composed of the papers resulting from the NATO work-shop "Perspectives in Ring Theory" and the work-shop "Geometry and Invariant The ory of Representations of Quivers" . Three reports on problem sessions have been induced in the part corresponding to the work-shop where they belonged. One more report on a problem session, the "lost" problem session, will be published elsewhere eventually. vii Acknowledgement The meeting became possible by the financial support of the Scientific Affairs Division of NATO. The people at this division have been very helpful in the orga nization of the meeting, in particular we commemorate Dr. Mario di Lullo, who died unexpectedly last year, but who has been very helpful with the organization of earlier meetings in Ring Theory. For additional financial support we thank the national foundation for scientific research (NFWO), the rector of the University of Antwerp, UIA, and the Belgian Ministry of Education. We also gladly acknowledge support from the Belgian Friends of the Hebrew University and the chairman Prof. P. Van Remoortere who honored Prof. S. Amitsur for his continuous contributions to the mathematical activities at the University of Antwerp. I thank the authors who contributed their paper(s) to this proceedings and the lecturers for their undisposable contributions towards the success of the work-shop. Finally I thank Danielle for allowing me to spoil another holiday period in favor of a congress.

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

Multiplication Objects in Monoidal Categories

Multiplication Objects in Monoidal Categories
Author: José Escoriza López
Publisher: Nova Publishers
Total Pages: 206
Release: 2000
Genre: Mathematics
ISBN: 9781560728238

The main aim of this book is to study the concept of multiplication objects from a categorical point of view, namely, in the setting of monoidal categories which are responsible for the narrow relationship between quantum groups and knot theory. At the same time, the book brings together the literature on multiplication modules and rings, which has been scattered to date. This book organises and exposes them in a categorical framework by using functorial techniques. Multiplication modules and rings are framed inside commutative algebra, which is a basis for number theory and algebraic geometry. These include families of rings very important in ideal arithmetic such as regular von Neumann rings, Dedekind domains, hereditary rings or special primary rings. In the relative case, i.e., multiplication modules and rings with respect to a hereditary torsion theory, the most significant example is that of Krull domains (with respect to the classical torsion theory). As a consequence, we have an adequate setting to consider divisorial properties. As for the graded concept, it is possible to examine deep in the study of arithmetically graded rings such as generalized Rees rings, graded Dedekind domains, twisted group rings, etc. The book points out some different possibilities to deal with the topic, for example, semiring theory, lattice theory, comodule theory, etc.

Infinite Crossed Products

Infinite Crossed Products
Author: Donald S. Passman
Publisher: Courier Corporation
Total Pages: 484
Release: 2013-07-24
Genre: Mathematics
ISBN: 0486315940

This groundbreaking monograph in advanced algebra addresses crossed products, which involve group and ring theory and the study of infinite group algebras, group-graded rings, and the Galois theory of noncommutative rings. 1989 edition.

Fixed Point Theory

Fixed Point Theory
Author: E. Fadell
Publisher: Springer
Total Pages: 524
Release: 2006-11-14
Genre: Mathematics
ISBN: 3540386009