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Author: C. Nastasescu
Publisher: Elsevier
ISBN: 0080960162
Category : Mathematics
Languages : en
Pages : 351
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Book Description
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: C. Nastasescu
Publisher: Elsevier
ISBN: 0080960162
Category : Mathematics
Languages : en
Pages : 351
Get Book
Book Description
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 Nastasescu
Publisher: Springer Science & Business Media
ISBN: 9783540207467
Category : Mathematics
Languages : en
Pages : 324
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Book Description
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: Roozbeh Hazrat
Publisher: Cambridge University Press
ISBN: 1316619583
Category : Mathematics
Languages : en
Pages : 244
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Book Description
This study of graded rings includes the first systematic account of the graded Grothendieck group, a powerful and crucial invariant in algebra which has recently been adopted to classify the Leavitt path algebras. The book begins with a concise introduction to the theory of graded rings and then focuses in more detail on Grothendieck groups, Morita theory, Picard groups and K-theory. The author extends known results in the ungraded case to the graded setting and gathers together important results which are currently scattered throughout the literature. The book is suitable for advanced undergraduate and graduate students, as well as researchers in ring theory.
Author: Constantin Nastasescu
Publisher:
ISBN:
Category :
Languages : en
Pages : 340
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Book Description
Author: Stefaan Caenepeel
Publisher: CRC Press
ISBN: 1000103781
Category : Mathematics
Languages : en
Pages : 280
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Book Description
This book introduces various notions defined in graded terms extending the notions most frequently used as basic ingredients in the theory of Azumaya algebras: separability and Galois extensions of commutative rings, crossed products and Galois cohomology, Picard groups, and the Brauer group.
Author: Constantin Năstăsescu
Publisher:
ISBN:
Category : Algebra
Languages : en
Pages : 304
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Book Description
Author: C. Nastasescu
Publisher: Springer
ISBN: 3540384782
Category : Mathematics
Languages : en
Pages : 159
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Book Description
Anesthesia Student Survival Guide: A Case-Based Approach is an indispensable introduction to the specialty. This concise, easy-to-read, affordable handbook is ideal for medical students, nursing students, and others during the anesthesia rotation. Written in a structured prose format and supplemented with many diagrams, tables, and algorithms, this pocket-sized guide contains essential material covered on the USMLE II-III and other licensing exams. The editors, who are academic faculty at Harvard Medical School, summarize the essential content with 32 informative and compelling case studies designed to help students apply new concepts to real situations. Pharmacology, basic skills, common procedures and anesthesia subspecialties are covered, too, with just the right amount of detail for an introductory text. The unique book also offers a section containing career advice and insider tips on how to receive good evaluations from supervising physicians. With its combination of astute clinical instruction, basic science explanation, and practical tips from physicians that have been there before, this handbook is your one-stop guide to a successful anesthesia rotation.
Author: Andrei V. Kelarev
Publisher: World Scientific
ISBN: 9812799729
Category : Mathematics
Languages : en
Pages : 218
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Book Description
This book contains the definitions of several ring constructions used in various applications. The concept of a groupoid-graded ring includes many of these constructions as special cases and makes it possible to unify the exposition. Recent research results on groupoid-graded rings and more specialized constructions are presented. In addition, there is a chapter containing open problems currently considered in the literature. Ring Constructions and Applications can serve as an excellent introduction for graduate students to many ring constructions as well as to essential basic concepts of group, semigroup and ring theories used in proofs. Contents: Preliminaries; Graded Rings; Examples of Ring Constructions; The Jacobson Radical; Groups of Units; Finiteness Conditions; PI-Rings and Varieties; Gradings of Matrix Rings; Examples of Applications; Open Problems. Readership: Graduate students and researchers using ring constructions in their work.
Author: Robert Wisbauer
Publisher: Routledge
ISBN: 1351447343
Category : Mathematics
Languages : en
Pages : 425
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Book Description
This volume provides a comprehensive introduction to module theory and the related part of ring theory, including original results as well as the most recent work. It is a useful and stimulating study for those new to the subject as well as for researchers and serves as a reference volume. Starting form a basic understanding of linear algebra, the theory is presented and accompanied by complete proofs. For a module M, the smallest Grothendieck category containing it is denoted by o[M] and module theory is developed in this category. Developing the techniques in o[M] is no more complicated than in full module categories and the higher generality yields significant advantages: for example, module theory may be developed for rings without units and also for non-associative rings. Numerous exercises are included in this volume to give further insight into the topics covered and to draw attention to related results in the literature.
Author: Paul E. Bland
Publisher: Walter de Gruyter
ISBN: 3110250225
Category : Mathematics
Languages : en
Pages : 467
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Book Description
This book is an introduction to the theory of rings and modules that goes beyond what one normally obtains in a graduate course in abstract algebra. In addition to the presentation of standard topics in ring and module theory, it also covers category theory, homological algebra and even more specialized topics like injective envelopes and proj
