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Local Rings
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Book Synopsis Lecture Notes On Local Rings by : Birger Iversen
Download or read book Lecture Notes On Local Rings written by Birger Iversen and published by World Scientific. This book was released on 2014-06-20 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: The content in Chapter 1-3 is a fairly standard one-semester course on local rings with the goal to reach the fact that a regular local ring is a unique factorization domain. The homological machinery is also supported by Cohen-Macaulay rings and depth. In Chapters 4-6 the methods of injective modules, Matlis duality and local cohomology are discussed. Chapters 7-9 are not so standard and introduce the reader to the generalizations of modules to complexes of modules. Some of Professor Iversen's results are given in Chapter 9. Chapter 10 is about Serre's intersection conjecture. The graded case is fully exposed. The last chapter introduces the reader to Fitting ideals and McRae invariants.
Download or read book Local Rings written by Masayoshi Nagata and published by . This book was released on 1975 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
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.
Book Synopsis Geometric Algebra Over Local Rings by : Bernard R. McDonald
Download or read book Geometric Algebra Over Local Rings written by Bernard R. McDonald and published by . This book was released on 1976 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Local Fields written by Jean-Pierre Serre and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of this book is to present local class field theory from the cohomo logical point of view, following the method inaugurated by Hochschild and developed by Artin-Tate. This theory is about extensions-primarily abelian-of "local" (i.e., complete for a discrete valuation) fields with finite residue field. For example, such fields are obtained by completing an algebraic number field; that is one of the aspects of "localisation". The chapters are grouped in "parts". There are three preliminary parts: the first two on the general theory of local fields, the third on group coho mology. Local class field theory, strictly speaking, does not appear until the fourth part. Here is a more precise outline of the contents of these four parts: The first contains basic definitions and results on discrete valuation rings, Dedekind domains (which are their "globalisation") and the completion process. The prerequisite for this part is a knowledge of elementary notions of algebra and topology, which may be found for instance in Bourbaki. The second part is concerned with ramification phenomena (different, discriminant, ramification groups, Artin representation). Just as in the first part, no assumptions are made here about the residue fields. It is in this setting that the "norm" map is studied; I have expressed the results in terms of "additive polynomials" and of "multiplicative polynomials", since using the language of algebraic geometry would have led me too far astray.
Book Synopsis Commutative Ring Theory by : Hideyuki Matsumura
Download or read book Commutative Ring Theory written by Hideyuki Matsumura and published by Cambridge University Press. This book was released on 1989-05-25 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores commutative ring theory, an important a foundation for algebraic geometry and complex analytical geometry.
Author :Thiruvalloor E. Venkata Balaji Publisher :Universitätsverlag Göttingen ISBN 13 :3941875329 Total Pages :241 pages Book Rating :4.9/5 (418 download)
Book Synopsis An Introduction to Families, Deformations and Moduli by : Thiruvalloor E. Venkata Balaji
Download or read book An Introduction to Families, Deformations and Moduli written by Thiruvalloor E. Venkata Balaji and published by Universitätsverlag Göttingen. This book was released on 2010 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: Moduli Theory is one of those areas of Mathematics that has fascinated minds from classical to modern times. This has been so because it reveals beautiful Geometry naturally hidden in questions involving classification of geometric objects and because of the profound use of the methods of several areas of Mathematics like Algebra, Number Theory, Topology and Analysis to achieve this revelation. A study of Moduli Theory would therefore give senior undergraduate and graduate students an integrated view of Mathematics. The present book is a humble introduction to some aspects of Moduli Theory.
Download or read book Topological Rings written by S. Warner and published by Elsevier. This book was released on 1993-07-07 with total page 509 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text brings the reader to the frontiers of current research in topological rings. The exercises illustrate many results and theorems while a comprehensive bibliography is also included. The book is aimed at those readers acquainted with some very basic point-set topology and algebra, as normally presented in semester courses at the beginning graduate level or even at the advanced undergraduate level. Familiarity with Hausdorff, metric, compact and locally compact spaces and basic properties of continuous functions, also with groups, rings, fields, vector spaces and modules, and with Zorn's Lemma, is also expected.
Book Synopsis Finite Commutative Rings and Their Applications by : Gilberto Bini
Download or read book Finite Commutative Rings and Their Applications written by Gilberto Bini and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 181 pages. Available in PDF, EPUB and Kindle. Book excerpt: Foreword by Dieter Jungnickel Finite Commutative Rings and their Applications answers a need for an introductory reference in finite commutative ring theory as applied to information and communication theory. This book will be of interest to both professional and academic researchers in the fields of communication and coding theory. The book is a concrete and self-contained introduction to finite commutative local rings, focusing in particular on Galois and Quasi-Galois rings. The reader is provided with an active and concrete approach to the study of the purely algebraic structure and properties of finite commutative rings (in particular, Galois rings) as well as to their applications to coding theory. Finite Commutative Rings and their Applications is the first to address both theoretical and practical aspects of finite ring theory. The authors provide a practical approach to finite rings through explanatory examples, thereby avoiding an abstract presentation of the subject. The section on Quasi-Galois rings presents new and unpublished results as well. The authors then introduce some applications of finite rings, in particular Galois rings, to coding theory, using a solid algebraic and geometric theoretical background.
Book Synopsis The Concise Handbook of Algebra by : Alexander V. Mikhalev
Download or read book The Concise Handbook of Algebra written by Alexander V. Mikhalev and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 629 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is by no means clear what comprises the "heart" or "core" of algebra, the part of algebra which every algebraist should know. Hence we feel that a book on "our heart" might be useful. We have tried to catch this heart in a collection of about 150 short sections, written by leading algebraists in these areas. These sections are organized in 9 chapters A, B, . . . , I. Of course, the selection is partly based on personal preferences, and we ask you for your understanding if some selections do not meet your taste (for unknown reasons, we only had problems in the chapter "Groups" to get enough articles in time). We hope that this book sets up a standard of what all algebraists are supposed to know in "their" chapters; interested people from other areas should be able to get a quick idea about the area. So the target group consists of anyone interested in algebra, from graduate students to established researchers, including those who want to obtain a quick overview or a better understanding of our selected topics. The prerequisites are something like the contents of standard textbooks on higher algebra. This book should also enable the reader to read the "big" Handbook (Hazewinkel 1999-) and other handbooks. In case of multiple authors, the authors are listed alphabetically; so their order has nothing to do with the amounts of their contributions.
Book Synopsis Integral Domains Inside Noetherian Power Series Rings: Constructions and Examples by : William Heinzer
Download or read book Integral Domains Inside Noetherian Power Series Rings: Constructions and Examples written by William Heinzer and published by American Mathematical Soc.. This book was released on 2021-10-08 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: Power series provide a technique for constructing examples of commutative rings. In this book, the authors describe this technique and use it to analyse properties of commutative rings and their spectra. This book presents results obtained using this approach. The authors put these results in perspective; often the proofs of properties of classical examples are simplified. The book will serve as a helpful resource for researchers working in commutative algebra.
Book Synopsis Graphs from Rings by : David F. Anderson
Download or read book Graphs from Rings written by David F. Anderson and published by Springer Nature. This book was released on 2021-10-31 with total page 548 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives an overview of research on graphs associated with commutative rings. The study of the connections between algebraic structures and certain graphs, especially finite groups and their Cayley graphs, is a classical subject which has attracted a lot of interest. More recently, attention has focused on graphs constructed from commutative rings, a field of study which has generated an extensive amount of research over the last three decades. The aim of this text is to consolidate this large body of work into a single volume, with the intention of encouraging interdisciplinary research between algebraists and graph theorists, using the tools of one subject to solve the problems of the other. The topics covered include the graphical and topological properties of zero-divisor graphs, total graphs and their transformations, and other graphs associated with rings. The book will be of interest to researchers in commutative algebra and graph theory and anyone interested in learning about the connections between these two subjects.
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
Book Synopsis A First Course in Noncommutative Rings by : T.Y. Lam
Download or read book A First Course in Noncommutative Rings written by T.Y. Lam and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of my favorite graduate courses at Berkeley is Math 251, a one-semester course in ring theory offered to second-year level graduate students. I taught this course in the Fall of 1983, and more recently in the Spring of 1990, both times focusing on the theory of noncommutative rings. This book is an outgrowth of my lectures in these two courses, and is intended for use by instructors and graduate students in a similar one-semester course in basic ring theory. Ring theory is a subject of central importance in algebra. Historically, some of the major discoveries in ring theory have helped shape the course of development of modern abstract algebra. Today, ring theory is a fer tile meeting ground for group theory (group rings), representation theory (modules), functional analysis (operator algebras), Lie theory (enveloping algebras), algebraic geometry (finitely generated algebras, differential op erators, invariant theory), arithmetic (orders, Brauer groups), universal algebra (varieties of rings), and homological algebra (cohomology of rings, projective modules, Grothendieck and higher K-groups). In view of these basic connections between ring theory and other branches of mathemat ics, it is perhaps no exaggeration to say that a course in ring theory is an indispensable part of the education for any fledgling algebraist. The purpose of my lectures was to give a general introduction to the theory of rings, building on what the students have learned from a stan dard first-year graduate course in abstract algebra.
Book Synopsis Complete Ideals in Regular Local Rings of Dimension 2 by : Oscar Zariski
Download or read book Complete Ideals in Regular Local Rings of Dimension 2 written by Oscar Zariski and published by . This book was released on 1959 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Foundations of Commutative Rings and Their Modules by : Fanggui Wang
Download or read book Foundations of Commutative Rings and Their Modules written by Fanggui Wang and published by Springer. This book was released on 2017-01-06 with total page 714 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to the basics and recent developments of commutative algebra. A glance at the contents of the first five chapters shows that the topics covered are ones that usually are included in any commutative algebra text. However, the contents of this book differ significantly from most commutative algebra texts: namely, its treatment of the Dedekind–Mertens formula, the (small) finitistic dimension of a ring, Gorenstein rings, valuation overrings and the valuative dimension, and Nagata rings. Going further, Chapter 6 presents w-modules over commutative rings as they can be most commonly used by torsion theory and multiplicative ideal theory. Chapter 7 deals with multiplicative ideal theory over integral domains. Chapter 8 collects various results of the pullbacks, especially Milnor squares and D+M constructions, which are probably the most important example-generating machines. In Chapter 9, coherent rings with finite weak global dimensions are probed, and the local ring of weak global dimension two is elaborated on by combining homological tricks and methods of star operation theory. Chapter 10 is devoted to the Grothendieck group of a commutative ring. In particular, the Bass–Quillen problem is discussed. Finally, Chapter 11 aims to introduce relative homological algebra, especially where the related concepts of integral domains which appear in classical ideal theory are defined and investigated by using the class of Gorenstein projective modules. Each section of the book is followed by a selection of exercises of varying degrees of difficulty. This book will appeal to a wide readership from graduate students to academic researchers who are interested in studying commutative algebra.
