Lecture Notes On Local Rings
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Lecture Notes On Local Rings
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Author : Birger Iversen
language : en
Publisher: World Scientific
Release Date : 2014-06-20
Lecture Notes On Local Rings written by Birger Iversen and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-20 with Mathematics categories.
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.
Integral Closure Of Ideals Rings And Modules
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Author : Craig Huneke
language : en
Publisher: Cambridge University Press
Release Date : 2006-10-12
Integral Closure Of Ideals Rings And Modules written by Craig Huneke and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-10-12 with Mathematics categories.
Ideal for graduate students and researchers, this book presents a unified treatment of the central notions of integral closure.
Local Algebra
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Author : Jean-Pierre Serre
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Local Algebra written by Jean-Pierre Serre and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The present book is an English translation of Algebre Locale - Multiplicites published by Springer-Verlag as no. 11 of the Lecture Notes series. The original text was based on a set of lectures, given at the College de France in 1957-1958, and written up by Pierre Gabriel. Its aim was to give a short account of Commutative Algebra, with emphasis on the following topics: a) Modules (as opposed to Rings, which were thought to be the only subject of Commutative Algebra, before the emergence of sheaf theory in the 1950s); b) H omological methods, a la Cartan-Eilenberg; c) Intersection multiplicities, viewed as Euler-Poincare characteristics. The English translation, done with great care by Chee Whye Chin, differs from the original in the following aspects: - The terminology has been brought up to date (e.g. "cohomological dimension" has been replaced by the now customary "depth"). I have rewritten a few proofs and clarified (or so I hope) a few more. - A section on graded algebras has been added (App. III to Chap. IV). - New references have been given, especially to other books on Commu- tive Algebra: Bourbaki (whose Chap. X has now appeared, after a 40-year wait) , Eisenbud, Matsumura, Roberts, .... I hope that these changes will make the text easier to read, without changing its informal "Lecture Notes" character.
Lectures On The Asymptotic Theory Of Ideals
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Author : D. Rees
language : en
Publisher: Cambridge University Press
Release Date : 1988-11-25
Lectures On The Asymptotic Theory Of Ideals written by D. Rees and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988-11-25 with Mathematics categories.
In this book Professor Rees introduces and proves some of the main results of the asymptotic theory of ideals. The author's aim is to prove his Valuation Theorem, Strong Valuation Theorem, and Degree Formula, and to develop their consequences. The last part of the book is devoted to mixed multiplicities. Here the author develops his theory of general elements of ideals and gives a proof of a generalised degree formula. The reader is assumed to be familiar with basic commutative algebra, as covered in the standard texts, but the presentation is suitable for advanced graduate students. The work is an expansion of lectures given at Nagoya University.
Commutative Ring Theory
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Author : Hideyuki Matsumura
language : en
Publisher: Cambridge University Press
Release Date : 1989-05-25
Commutative Ring Theory written by Hideyuki Matsumura and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989-05-25 with Mathematics categories.
This book explores commutative ring theory, an important a foundation for algebraic geometry and complex analytical geometry.
Six Lectures On Commutative Algebra
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Author : J. Elias
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-03-17
Six Lectures On Commutative Algebra written by J. Elias and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-03-17 with Mathematics categories.
Interest in commutative algebra has surged over the past decades. In order to survey and highlight recent developments in this rapidly expanding field, the Centre de Recerca Matematica in Bellaterra organized a ten-days Summer School on Commutative Algebra in 1996. Lectures were presented by six high-level specialists, L. Avramov (Purdue), M.K. Green (UCLA), C. Huneke (Purdue), P. Schenzel (Halle), G. Valla (Genova) and W.V. Vasconcelos (Rutgers), providing a fresh and extensive account of the results, techniques and problems of some of the most active areas of research. The present volume is a synthesis of the lectures given by these authors. Research workers as well as graduate students in commutative algebra and nearby areas will find a useful overview of the field and recent developments in it. Reviews "All six articles are at a very high level; they provide a thorough survey of results and methods in their subject areas, illustrated with algebraic or geometric examples." - Acta Scientiarum Mathematicarum Avramov lecture: "... it contains all the major results [on infinite free resolutions], it explains carefully all the different techniques that apply, it provides complete proofs (...). This will be extremely helpful for the novice as well as the experienced." - Mathematical reviews Huneke lecture: "The topic is tight closure, a theory developed by M. Hochster and the author which has in a short time proved to be a useful and powerful tool. (...) The paper is extremely well organized, written, and motivated." - Zentralblatt MATH Schenzel lecture: "... this paper is an excellent introduction to applications of local cohomology." - Zentralblatt MATH Valla lecture: "... since he is an acknowledged expert on Hilbert functions and since his interest has been so broad, he has done a superb job in giving the readers a lively picture of the theory." - Mathematical reviews Vasconcelos lecture: "This is a very useful survey on invariants of modules over noetherian rings, relations between them, and how to compute them." - Zentralblatt MATH
Commutative Ring Theory
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Author : Paul-Jean Cahen
language : en
Publisher: CRC Press
Release Date : 2023-06-14
Commutative Ring Theory written by Paul-Jean Cahen and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-06-14 with Mathematics categories.
Presents the proceedings of the Second International Conference on Commutative Ring Theory in Fes, Morocco. The text details developments in commutative algebra, highlighting the theory of rings and ideals. It explores commutative algebra's connections with and applications to topological algebra and algebraic geometry.
Exercises In Modules And Rings
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Author : T.Y. Lam
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-12-15
Exercises In Modules And Rings written by T.Y. Lam and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-12-15 with Mathematics categories.
This volume offers a compendium of exercises of varying degree of difficulty in the theory of modules and rings. It is the companion volume to GTM 189. All exercises are solved in full detail. Each section begins with an introduction giving the general background and the theoretical basis for the problems that follow.
Lecture Notes In Algebraic Topology
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Author : James Frederic Davis
language : en
Publisher: American Mathematical Soc.
Release Date : 2001
Lecture Notes In Algebraic Topology written by James Frederic Davis and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.
The amount of algebraic topology a graduate student specializing in topology must learn can be intimidating. Moreover, by their second year of graduate studies, students must make the transition from understanding simple proofs line-by-line to understanding the overall structure of proofs of difficult theorems. To help students make this transition, the material in this book is presented in an increasingly sophisticated manner. It is intended to bridge the gap between algebraic andgeometric topology, both by providing the algebraic tools that a geometric topologist needs and by concentrating on those areas of algebraic topology that are geometrically motivated. Prerequisites for using this book include basic set-theoretic topology, the definition of CW-complexes, someknowledge of the fundamental group/covering space theory, and the construction of singular homology. Most of this material is briefly reviewed at the beginning of the book. The topics discussed by the authors include typical material for first- and second-year graduate courses. The core of the exposition consists of chapters on homotopy groups and on spectral sequences. There is also material that would interest students of geometric topology (homology with local coefficients and obstructiontheory) and algebraic topology (spectra and generalized homology), as well as preparation for more advanced topics such as algebraic $K$-theory and the s-cobordism theorem. A unique feature of the book is the inclusion, at the end of each chapter, of several projects that require students to presentproofs of substantial theorems and to write notes accompanying their explanations. Working on these projects allows students to grapple with the ``big picture'', teaches them how to give mathematical lectures, and prepares them for participating in research seminars. The book is designed as a textbook for graduate students studying algebraic and geometric topology and homotopy theory. It will also be useful for students from other fields such as differential geometry, algebraic geometry, andhomological algebra. The exposition in the text is clear; special cases are presented over complex general statements.
Algebra Algebraic Topology And Their Interactions
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Author : Jan-Erik Roos
language : en
Publisher: Springer
Release Date : 2006-11-14
Algebra Algebraic Topology And Their Interactions written by Jan-Erik Roos and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.