Graded Ring Theory

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Graded Ring Theory

Author : C. Nastasescu
Publisher : Elsevier
ISBN 13 : 0080960162
Total Pages : 351 pages
Book Rating : 4.0/5 (89 download)

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Book Synopsis Graded Ring Theory by : C. Nastasescu

Download or read book Graded Ring Theory written by C. Nastasescu and published by Elsevier. This book was released on 2011-08-18 with total page 351 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Methods of Graded Rings

Author : Constantin Nastasescu
Publisher : Springer Science & Business Media
ISBN 13 : 9783540207467
Total Pages : 324 pages
Book Rating : 4.2/5 (74 download)

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Book Synopsis Methods of Graded Rings by : Constantin Nastasescu

Download or read book Methods of Graded Rings written by Constantin Nastasescu and published by Springer Science & Business Media. This book was released on 2004-02-19 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.-

Graded Rings and Graded Grothendieck Groups

Author : Roozbeh Hazrat
Publisher : Cambridge University Press
ISBN 13 : 1316619583
Total Pages : 244 pages
Book Rating : 4.3/5 (166 download)

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Book Synopsis Graded Rings and Graded Grothendieck Groups by : Roozbeh Hazrat

Download or read book Graded Rings and Graded Grothendieck Groups written by Roozbeh Hazrat and published by Cambridge University Press. This book was released on 2016-05-26 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Graded Ring Theory

Author : Constantin Nastasescu
Publisher :
ISBN 13 :
Total Pages : 340 pages
Book Rating : 4.:/5 (859 download)

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Book Synopsis Graded Ring Theory by : Constantin Nastasescu

Download or read book Graded Ring Theory written by Constantin Nastasescu and published by . This book was released on 1982 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Brauer Groups and the Cohomology of Graded Rings

Author : Stefaan Caenepeel
Publisher : CRC Press
ISBN 13 : 1000103781
Total Pages : 280 pages
Book Rating : 4.0/5 (1 download)

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Book Synopsis Brauer Groups and the Cohomology of Graded Rings by : Stefaan Caenepeel

Download or read book Brauer Groups and the Cohomology of Graded Rings written by Stefaan Caenepeel and published by CRC Press. This book was released on 2020-08-26 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Rings and Their Modules

Author : Paul E. Bland
Publisher : Walter de Gruyter
ISBN 13 : 3110250225
Total Pages : 467 pages
Book Rating : 4.1/5 (12 download)

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Book Synopsis Rings and Their Modules by : Paul E. Bland

Download or read book Rings and Their Modules written by Paul E. Bland and published by Walter de Gruyter. This book was released on 2011 with total page 467 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Foundations of Module and Ring Theory

Author : Robert Wisbauer
Publisher : Routledge
ISBN 13 : 1351447343
Total Pages : 425 pages
Book Rating : 4.3/5 (514 download)

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Book Synopsis Foundations of Module and Ring Theory by : Robert Wisbauer

Download or read book Foundations of Module and Ring Theory written by Robert Wisbauer and published by Routledge. This book was released on 2018-05-11 with total page 425 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Introduction To Commutative Algebra

Author : Michael F. Atiyah
Publisher : CRC Press
ISBN 13 : 0429973268
Total Pages : 140 pages
Book Rating : 4.4/5 (299 download)

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Book Synopsis Introduction To Commutative Algebra by : Michael F. Atiyah

Download or read book Introduction To Commutative Algebra written by Michael F. Atiyah and published by CRC Press. This book was released on 2018-03-09 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: First Published in 2018. This book grew out of a course of lectures given to third year undergraduates at Oxford University and it has the modest aim of producing a rapid introduction to the subject. It is designed to be read by students who have had a first elementary course in general algebra. On the other hand, it is not intended as a substitute for the more voluminous tracts such as Zariski-Samuel or Bourbaki. We have concentrated on certain central topics, and large areas, such as field theory, are not touched. In content we cover rather more ground than Northcott and our treatment is substantially different in that, following the modern trend, we put more emphasis on modules and localization.

Ring Constructions and Applications

Author : Andrei V. Kelarev
Publisher : World Scientific
ISBN 13 : 9810247451
Total Pages : 218 pages
Book Rating : 4.8/5 (12 download)

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Book Synopsis Ring Constructions and Applications by : Andrei V. Kelarev

Download or read book Ring Constructions and Applications written by Andrei V. Kelarev and published by World Scientific. This book was released on 2002 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Leavitt Path Algebras

Author : Gene Abrams
Publisher : Springer
ISBN 13 : 1447173449
Total Pages : 289 pages
Book Rating : 4.4/5 (471 download)

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Book Synopsis Leavitt Path Algebras by : Gene Abrams

Download or read book Leavitt Path Algebras written by Gene Abrams and published by Springer. This book was released on 2017-11-30 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a comprehensive introduction by three of the leading experts in the field, collecting fundamental results and open problems in a single volume. Since Leavitt path algebras were first defined in 2005, interest in these algebras has grown substantially, with ring theorists as well as researchers working in graph C*-algebras, group theory and symbolic dynamics attracted to the topic. Providing a historical perspective on the subject, the authors review existing arguments, establish new results, and outline the major themes and ring-theoretic concepts, such as the ideal structure, Z-grading and the close link between Leavitt path algebras and graph C*-algebras. The book also presents key lines of current research, including the Algebraic Kirchberg Phillips Question, various additional classification questions, and connections to noncommutative algebraic geometry. Leavitt Path Algebras will appeal to graduate students and researchers working in the field and related areas, such as C*-algebras and symbolic dynamics. With its descriptive writing style, this book is highly accessible.

Graded and Filtered Rings and Modules

Author : C. Nastasescu
Publisher : Springer
ISBN 13 : 3540384782
Total Pages : 159 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Graded and Filtered Rings and Modules by : C. Nastasescu

Download or read book Graded and Filtered Rings and Modules written by C. Nastasescu and published by Springer. This book was released on 2006-11-15 with total page 159 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Methods of Graded Rings

Author : Constantin Năstăsescu
Publisher :
ISBN 13 :
Total Pages : 304 pages
Book Rating : 4.:/5 (61 download)

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Book Synopsis Methods of Graded Rings by : Constantin Năstăsescu

Download or read book Methods of Graded Rings written by Constantin Năstăsescu and published by . This book was released on 2004 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Ring Constructions and Applications

Author : Andrei V. Kelarev
Publisher : World Scientific
ISBN 13 : 9812799729
Total Pages : 218 pages
Book Rating : 4.8/5 (127 download)

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Book Synopsis Ring Constructions and Applications by : Andrei V. Kelarev

Integral Closure of Ideals, Rings, and Modules

Author : Craig Huneke
Publisher : Cambridge University Press
ISBN 13 : 0521688604
Total Pages : 446 pages
Book Rating : 4.5/5 (216 download)

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Book Synopsis Integral Closure of Ideals, Rings, and Modules by : Craig Huneke

Download or read book Integral Closure of Ideals, Rings, and Modules written by Craig Huneke and published by Cambridge University Press. This book was released on 2006-10-12 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ideal for graduate students and researchers, this book presents a unified treatment of the central notions of integral closure.

Commutative Ring Theory and Applications

Author : Marco Fontana
Publisher : CRC Press
ISBN 13 : 9780203910627
Total Pages : 524 pages
Book Rating : 4.9/5 (16 download)

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Book Synopsis Commutative Ring Theory and Applications by : Marco Fontana

Download or read book Commutative Ring Theory and Applications written by Marco Fontana and published by CRC Press. This book was released on 2017-07-27 with total page 524 pages. Available in PDF, EPUB and Kindle. Book excerpt: Featuring presentations from the Fourth International Conference on Commutative Algebra held in Fez, Morocco, this reference presents trends in the growing area of commutative algebra. With contributions from nearly 50 internationally renowned researchers, the book emphasizes innovative applications and connections to algebraic number theory, geome

Commutative Algebra

Author : David Eisenbud
Publisher : Springer Science & Business Media
ISBN 13 : 1461253500
Total Pages : 784 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Commutative Algebra by : David Eisenbud

Download or read book Commutative Algebra written by David Eisenbud and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 784 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a comprehensive review of commutative algebra, from localization and primary decomposition through dimension theory, homological methods, free resolutions and duality, emphasizing the origins of the ideas and their connections with other parts of mathematics. The book gives a concise treatment of Grobner basis theory and the constructive methods in commutative algebra and algebraic geometry that flow from it. Many exercises included.

Determinantal Rings

Author : Winfried Bruns
Publisher : Springer
ISBN 13 : 3540392742
Total Pages : 246 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Determinantal Rings by : Winfried Bruns

Download or read book Determinantal Rings written by Winfried Bruns and published by Springer. This book was released on 2006-11-14 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: Determinantal rings and varieties have been a central topic of commutative algebra and algebraic geometry. Their study has attracted many prominent researchers and has motivated the creation of theories which may now be considered part of general commutative ring theory. The book gives a first coherent treatment of the structure of determinantal rings. The main approach is via the theory of algebras with straightening law. This approach suggest (and is simplified by) the simultaneous treatment of the Schubert subvarieties of Grassmannian. Other methods have not been neglected, however. Principal radical systems are discussed in detail, and one section is devoted to each of invariant and representation theory. While the book is primarily a research monograph, it serves also as a reference source and the reader requires only the basics of commutative algebra together with some supplementary material found in the appendix. The text may be useful for seminars following a course in commutative ring theory since a vast number of notions, results, and techniques can be illustrated significantly by applying them to determinantal rings.