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Author: F. van Oystaeyen
Publisher: Springer
ISBN: 3540383344
Category : Mathematics
Languages : en
Pages : 220
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Author: F. van Oystaeyen
Publisher: Springer
ISBN: 3540383344
Category : Mathematics
Languages : en
Pages : 220
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Book Description
Author: C. Nastasescu
Publisher: Springer Science & Business Media
ISBN: 9400938357
Category : Mathematics
Languages : en
Pages : 369
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Book Description
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.
Author: K.P.S. Bhaskara Rao
Publisher: CRC Press
ISBN: 0203218876
Category : Mathematics
Languages : en
Pages : 193
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Book Description
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. The subject of generalized inverses of matrices over rings has now reached a state suitable for a comprehensive treatment - this book provides just that, for mathematicians, algebraists and control theorists.
Author: Freddy Van Oystaeyen
Publisher: Springer Science & Business Media
ISBN: 9400929854
Category : Mathematics
Languages : en
Pages : 386
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Book Description
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.
Author: C. Nastasescu
Publisher: Elsevier
ISBN: 0080960162
Category : Mathematics
Languages : en
Pages : 352
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This book is aimed to be a ‘technical’ book on graded rings. By ‘technical’ we mean that the book should supply a kit of tools of quite general applicability, enabling the reader to build up his own further study of non-commutative rings graded by an arbitrary group. The body of the book, Chapter A, contains: categorical properties of graded modules, localization of graded rings and modules, Jacobson radicals of graded rings, the structure thedry for simple objects in the graded sense, chain conditions, Krull dimension of graded modules, homogenization, homological dimension, primary decomposition, and more. One of the advantages of the generality of Chapter A is that it allows direct applications of these results to the theory of group rings, twisted and skew group rings and crossed products. With this in mind we have taken care to point out on several occasions how certain techniques may be specified to the case of strongly graded rings. We tried to write Chapter A in such a way that it becomes suitable for an advanced course in ring theory or general algebra, we strove to make it as selfcontained as possible and we included several problems and exercises. Other chapters may be viewed as an attempt to show how the general techniques of Chapter A can be applied in some particular cases, e.g. the case where the gradation is of type Z. In compiling the material for Chapters B and C we have been guided by our own research interests. Chapter 6 deals with commutative graded rings of type 2 and we focus on two main topics: artihmeticallygraded domains, and secondly, local conditions for Noetherian rings. In Chapter C we derive some structural results relating to the graded properties of the rings considered. The following classes of graded rings receive special attention: fully bounded Noetherian rings, birational extensions of commutative rings, rings satisfying polynomial identities, and Von Neumann regular rings. Here the basic idea is to derive results of ungraded nature from graded information. Some of these sections lead naturally to the study of sheaves over the projective spectrum Proj(R) of a positively graded ring, but we did not go into these topics here. We refer to [125] for a noncommutative treatment of projective geometry, i.e. the geometry of graded P.I. algebras.
Author: Freddy Van Oystaeyen
Publisher: Springer Science & Business Media
ISBN: 9400963696
Category : Mathematics
Languages : en
Pages : 569
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Book Description
Proceedings of the NATO Advanced Study Institute, Antwerp, Belgium, August 2-12, 1983
Author: M. Hazewinkel
Publisher: Elsevier
ISBN: 0080532969
Category : Mathematics
Languages : en
Pages : 899
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Book Description
Handbook of Algebra
Author: P. L. Garcia
Publisher: Springer
ISBN: 3540384057
Category : Mathematics
Languages : en
Pages : 551
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Book Description
Author: S. Shelah
Publisher: Springer
ISBN: 3662215438
Category : Mathematics
Languages : en
Pages : 528
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Book Description
These notes can be viewed and used in several different ways, each has some justification, a collection of papers, a research monograph or a text book. The author has lectured variants of several of the chapters several times: in University of California, Berkeley, 1978, Ch. III , N, V in Ohio State Univer sity in Columbus, Ohio 1979, Ch. I,ll and in the Hebrew University 1979/80 Ch. I, II, III, V, and parts of VI. Moreover Azriel Levi, who has a much better name than the author in such matters, made notes from the lectures in the Hebrew University, rewrote them, and they ·are Chapters I, II and part of III , and were somewhat corrected and expanded by D. Drai, R. Grossberg and the author. Also most of XI §1-5 were lectured on and written up by Shai Ben David. Also our presentation is quite self-contained. We adopted an approach I heard from Baumgartner and may have been used by others: not proving that forcing work, rather take axiomatically that it does and go ahead to applying it. As a result we assume only knowledge of naive set theory (except some iso lated points later on in the book).
Author: D. Ferus
Publisher: Springer
ISBN: 3540384197
Category : Mathematics
Languages : en
Pages : 312
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Book Description
