Methods Of Graded Rings PDF Download
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Author | : Constantin Nastasescu |
Publisher | : Springer Science & Business Media |
Total Pages | : 324 |
Release | : 2004-02-19 |
Genre | : Mathematics |
ISBN | : 9783540207467 |
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The Category of Graded Rings.- The Category of Graded Modules.- Modules over Stronly Graded Rings.- Graded Clifford Theory.- Internal Homogenization.- External Homogenization.- Smash Products.- Localization of Graded Rings.- Application to Gradability.- Appendix A:Some Category Theory.- Appendix B: Dimensions in an abelian Category.- Bibliography.- Index.-
Author | : C. Nastasescu |
Publisher | : Elsevier |
Total Pages | : 352 |
Release | : 2011-08-18 |
Genre | : Mathematics |
ISBN | : 0080960162 |
Download Graded Ring Theory Book in PDF, ePub and Kindle
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 | : Constantin Năstăsescu |
Publisher | : |
Total Pages | : 304 |
Release | : 2004 |
Genre | : Algebra |
ISBN | : |
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Author | : Constantin Nastasescu |
Publisher | : |
Total Pages | : 324 |
Release | : 2014-01-15 |
Genre | : |
ISBN | : 9783662211311 |
Download Methods of Graded Rings Book in PDF, ePub and Kindle
Author | : Freddy Van Oystaeyen |
Publisher | : Springer Science & Business Media |
Total Pages | : 569 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 9400963696 |
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Proceedings of the NATO Advanced Study Institute, Antwerp, Belgium, August 2-12, 1983
Author | : Pedro L. Garcia |
Publisher | : Springer |
Total Pages | : 307 |
Release | : 2006-11-15 |
Genre | : Mathematics |
ISBN | : 354047854X |
Download Differential Geometric Methods in Mathematical Physics Book in PDF, ePub and Kindle
The focal topic of the 14th International Conference on Differential Geometric Methods was that of mathematical problems in classical field theory and the emphasis of the resulting proceedings volume is on superfield theory and related topics, and classical and quantized fields.
Author | : Ştefan Ovidiu I. Tohăneanu |
Publisher | : Walter de Gruyter GmbH & Co KG |
Total Pages | : 276 |
Release | : 2024-07-01 |
Genre | : Mathematics |
ISBN | : 3111214796 |
Download Commutative Algebra Methods for Coding Theory Book in PDF, ePub and Kindle
This book aims to be a comprehensive treatise on the interactions between Coding Theory and Commutative Algebra. With the help of a multitude of examples, it expands and systematizes the known and versatile commutative algebraic framework used, since the early 90’s, to study linear codes. The book provides the necessary background for the reader to advance with similar research on coding theory topics from commutative algebraic perspectives.
Author | : Sergei I. Gelfand |
Publisher | : Springer Science & Business Media |
Total Pages | : 388 |
Release | : 2013-04-17 |
Genre | : Mathematics |
ISBN | : 3662032201 |
Download Methods of Homological Algebra Book in PDF, ePub and Kindle
Homological algebra first arose as a language for describing topological prospects of geometrical objects. As with every successful language it quickly expanded its coverage and semantics, and its contemporary applications are many and diverse. This modern approach to homological algebra, by two leading writers in the field, is based on the systematic use of the language and ideas of derived categories and derived functors. Relations with standard cohomology theory (sheaf cohomology, spectral sequences, etc.) are described. In most cases complete proofs are given. Basic concepts and results of homotopical algebra are also presented. The book addresses people who want to learn about a modern approach to homological algebra and to use it in their work.
Author | : Peter Falb |
Publisher | : Springer Science & Business Media |
Total Pages | : 382 |
Release | : 2013-12-01 |
Genre | : Mathematics |
ISBN | : 1461215641 |
Download Methods of Algebraic Geometry in Control Theory: Part II Book in PDF, ePub and Kindle
"Control theory represents an attempt to codify, in mathematical terms, the principles and techniques used in the analysis and design of control systems. Algebraic geometry may, in an elementary way, be viewed as the study of the structure and properties of the solutions of systems of algebraic equations. The aim of this book is to provide access to the methods of algebraic geometry for engineers and applied scientists through the motivated context of control theory" .* The development which culminated with this volume began over twenty-five years ago with a series of lectures at the control group of the Lund Institute of Technology in Sweden. I have sought throughout to strive for clarity, often using constructive methods and giving several proofs of a particular result as well as many examples. The first volume dealt with the simplest control systems (i.e., single input, single output linear time-invariant systems) and with the simplest algebraic geometry (i.e., affine algebraic geometry). While this is quite satisfactory and natural for scalar systems, the study of multi-input, multi-output linear time invariant control systems requires projective algebraic geometry. Thus, this second volume deals with multi-variable linear systems and pro jective algebraic geometry. The results are deeper and less transparent, but are also quite essential to an understanding of linear control theory. A review of * From the Preface to Part 1. viii Preface the scalar theory is included along with a brief summary of affine algebraic geometry (Appendix E).
Author | : Mel Schwartz |
Publisher | : CRC Press |
Total Pages | : 711 |
Release | : 2005-11-04 |
Genre | : Technology & Engineering |
ISBN | : 1420039342 |
Download New Materials, Processes, and Methods Technology Book in PDF, ePub and Kindle
Materials selection is a crucial factor in determining the cost, quality, and corrosion protection for every engineering project. The variety of increasingly durable materials and their combinations, coupled with the rise of new and more critical service requirements and the demand for lower costs, have expanded upon trial-and-error criteria into m