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Approximate Commutative Algebra
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Book Synopsis Approximate Commutative Algebra by : Lorenzo Robbiano
Download or read book Approximate Commutative Algebra written by Lorenzo Robbiano and published by Springer Science & Business Media. This book was released on 2009-09-18 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: Approximate Commutative Algebra is an emerging field of research which endeavours to bridge the gap between traditional exact Computational Commutative Algebra and approximate numerical computation. The last 50 years have seen enormous progress in the realm of exact Computational Commutative Algebra, and given the importance of polynomials in scientific modelling, it is very natural to want to extend these ideas to handle approximate, empirical data deriving from physical measurements of phenomena in the real world. In this volume nine contributions from established researchers describe various approaches to tackling a variety of problems arising in Approximate Commutative Algebra.
Book Synopsis Approximation Theorems in Commutative Algebra by : J. Alajbegovic
Download or read book Approximation Theorems in Commutative Algebra written by J. Alajbegovic and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: Various types of approximation theorems are frequently used in general commutative algebra, and they have been found to be useful tools in valuation theory, the theory of Abelian lattice ordered groups, multiplicative ideal theory, etc. Part 1 of this volume is devoted to the investigation of approximation theorems from a classical point of view. The chapters of this part deal with fields and rings, partly ordered groups, and with multirings and d-groups. Part II investigates approximation theorems from a general, categorical point of view. This part is essentially self-contained and requires only a basic knowledge of category theory and first-order logic. For researchers and graduate students of commutative algebra, category theory, as well as applications of logic.
Book Synopsis The Use of Ultraproducts in Commutative Algebra by : Hans Schoutens
Download or read book The Use of Ultraproducts in Commutative Algebra written by Hans Schoutens and published by Springer. This book was released on 2010-07-16 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt: In spite of some recent applications of ultraproducts in algebra, they remain largely unknown to commutative algebraists, in part because they do not preserve basic properties such as Noetherianity. This work wants to make a strong case against these prejudices. More precisely, it studies ultraproducts of Noetherian local rings from a purely algebraic perspective, as well as how they can be used to transfer results between the positive and zero characteristics, to derive uniform bounds, to define tight closure in characteristic zero, and to prove asymptotic versions of homological conjectures in mixed characteristic. Some of these results are obtained using variants called chromatic products, which are often even Noetherian. This book, neither assuming nor using any logical formalism, is intended for algebraists and geometers, in the hope of popularizing ultraproducts and their applications in algebra.
Book Synopsis Commutative Algebra by : J. William Hoffman
Download or read book Commutative Algebra written by J. William Hoffman and published by Mercury Learning and Information. This book was released on 2016-04-15 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this book is twofold: to present some basic ideas in commutative algebra and algebraic geometry and to introduce topics of current research, centered around the themes of Gröbner bases, resultants and syzygies. The presentation of the material combines definitions and proofs with an emphasis on concrete examples. The authors illustrate the use of software such as Mathematica and Singular. The design of the text in each chapter consists of two parts: the fundamentals and the applications, which make it suitable for courses of various lengths, levels, and topics based on the mathematical background of the students. The fundamentals portion of the chapter is intended to be read with minimal outside assistance, and to learn some of the most useful tools in commutative algebra. The applications of the chapter are to provide a glimpse of the advanced mathematical research where the topics and results are related to the material presented earlier. In the applications portion, the authors present a number of results from a wide range of sources without detailed proofs. The applications portion of the chapter is suitable for a reader who knows a little commutative algebra and algebraic geometry already, and serves as a guide to some interesting research topics. This book should be thought of as an introduction to more advanced texts and research topics. Its novelty is that the material presented is a unique combination of the essential methods and the current research results. The goal is to equip readers with the fundamental classical algebra and geometry tools, ignite their research interests, and initiate some potential research projects in the related areas.
Book Synopsis Recent Developments in Commutative Algebra by : Claudia Polini
Download or read book Recent Developments in Commutative Algebra written by Claudia Polini and published by Springer Nature. This book was released on 2021-03-02 with total page 127 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents four lectures on Rees rings and blow-ups, Koszul modules with applications to syzygies, Gröbner bases and degenerations, and applications of Adams operations. Commutative Algebra has witnessed a number of spectacular developments in recent years, including the resolution of long-standing problems; the new techniques and perspectives are leading to an extraordinary transformation in the field. The material contained in this volume, based on lectures given at a workshop held in Levico Terme, Trento, in July 2019, highlights some of these developments. The text will be a valuable asset to graduate students and researchers in commutative algebra and related fields.
Book Synopsis Commutative Algebra by : Irena Peeva
Download or read book Commutative Algebra written by Irena Peeva and published by Springer Science & Business Media. This book was released on 2013-02-01 with total page 705 pages. Available in PDF, EPUB and Kindle. Book excerpt: This contributed volume brings together the highest quality expository papers written by leaders and talented junior mathematicians in the field of Commutative Algebra. Contributions cover a very wide range of topics, including core areas in Commutative Algebra and also relations to Algebraic Geometry, Algebraic Combinatorics, Hyperplane Arrangements, Homological Algebra, and String Theory. The book aims to showcase the area, especially for the benefit of junior mathematicians and researchers who are new to the field; it will aid them in broadening their background and to gain a deeper understanding of the current research in this area. Exciting developments are surveyed and many open problems are discussed with the aspiration to inspire the readers and foster further research.
Book Synopsis Introduction to Commutative Algebra and Algebraic Geometry by : Ernst Kunz
Download or read book Introduction to Commutative Algebra and Algebraic Geometry written by Ernst Kunz and published by Springer Science & Business Media. This book was released on 2012-11-06 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt: Originally published in 1985, this classic textbook is an English translation of Einführung in die kommutative Algebra und algebraische Geometrie. As part of the Modern Birkhäuser Classics series, the publisher is proud to make Introduction to Commutative Algebra and Algebraic Geometry available to a wider audience. Aimed at students who have taken a basic course in algebra, the goal of the text is to present important results concerning the representation of algebraic varieties as intersections of the least possible number of hypersurfaces and—a closely related problem—with the most economical generation of ideals in Noetherian rings. Along the way, one encounters many basic concepts of commutative algebra and algebraic geometry and proves many facts which can then serve as a basic stock for a deeper study of these subjects.
Book Synopsis An Introduction to Commutative Algebra by : Huishi Li
Download or read book An Introduction to Commutative Algebra written by Huishi Li and published by World Scientific. This book was released on 2004 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: - Contains many examples and problems (with hints) - Provides a good introduction for beginners in algebraic number theory and algebraic geometry
Book Synopsis Algebraic Geometry and Commutative Algebra by : Hiroaki Hijikata
Download or read book Algebraic Geometry and Commutative Algebra written by Hiroaki Hijikata and published by Academic Press. This book was released on 2014-05-10 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebraic Geometry and Commutative Algebra in Honor of Masayoshi Nagata presents a collection of papers on algebraic geometry and commutative algebra in honor of Masayoshi Nagata for his significant contributions to commutative algebra. Topics covered range from power series rings and rings of invariants of finite linear groups to the convolution algebra of distributions on totally disconnected locally compact groups. The discussion begins with a description of several formulas for enumerating certain types of objects, which may be tabular arrangements of integers called Young tableaux or some types of monomials. The next chapter explains how to establish these enumerative formulas, with emphasis on the role played by transformations of determinantal polynomials and recurrence relations satisfied by them. The book then turns to several applications of the enumerative formulas and universal identity, including including enumerative proofs of the straightening law of Doubilet-Rota-Stein and computations of Hilbert functions of polynomial ideals of certain determinantal loci. Invariant differentials and quaternion extensions are also examined, along with the moduli of Todorov surfaces and the classification problem of embedded lines in characteristic p. This monograph will be a useful resource for practitioners and researchers in algebra and geometry.
Book Synopsis Commutative Algebra by : James Thomson Knight
Download or read book Commutative Algebra written by James Thomson Knight and published by Cambridge University Press. This book was released on 1971-10-31 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to commutative algebra gives an account of some general properties of rings and modules, with their applications to number theory and geometry. It assumes only that the reader has completed an undergraduate algebra course. The fresh approach and simplicity of proof enable a large amount of material to be covered; exercises and examples are included throughout the notes.
Book Synopsis A Singular Introduction to Commutative Algebra by : Gert-Martin Greuel
Download or read book A Singular Introduction to Commutative Algebra written by Gert-Martin Greuel and published by Springer Science & Business Media. This book was released on 2007-09-23 with total page 703 pages. Available in PDF, EPUB and Kindle. Book excerpt: This substantially enlarged second edition aims to lead a further stage in the computational revolution in commutative algebra. This is the first handbook/tutorial to extensively deal with SINGULAR. Among the book’s most distinctive features is a new, completely unified treatment of the global and local theories. Another feature of the book is its breadth of coverage of theoretical topics in the portions of commutative algebra closest to algebraic geometry, with algorithmic treatments of almost every topic.
Book Synopsis Approximations and Endomorphism Algebras of Modules by : Rüdiger Göbel
Download or read book Approximations and Endomorphism Algebras of Modules written by Rüdiger Göbel and published by Walter de Gruyter. This book was released on 2012-10-01 with total page 1002 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second, revised and substantially extended edition of Approximations and Endomorphism Algebras of Modules reflects both the depth and the width of recent developments in the area since the first edition appeared in 2006. The new division of the monograph into two volumes roughly corresponds to its two central topics, approximation theory (Volume 1) and realization theorems for modules (Volume 2). It is a widely accepted fact that the category of all modules over a general associative ring is too complex to admit classification. Unless the ring is of finite representation type we must limit attempts at classification to some restricted subcategories of modules. The wild character of the category of all modules, or of one of its subcategories C, is often indicated by the presence of a realization theorem, that is, by the fact that any reasonable algebra is isomorphic to the endomorphism algebra of a module from C. This results in the existence of pathological direct sum decompositions, and these are generally viewed as obstacles to classification. In order to overcome this problem, the approximation theory of modules has been developed. The idea here is to select suitable subcategories C whose modules can be classified, and then to approximate arbitrary modules by those from C. These approximations are neither unique nor functorial in general, but there is a rich supply available appropriate to the requirements of various particular applications. The authors bring the two theories together. The first volume, Approximations, sets the scene in Part I by introducing the main classes of modules relevant here: the S-complete, pure-injective, Mittag-Leffler, and slender modules. Parts II and III of the first volume develop the key methods of approximation theory. Some of the recent applications to the structure of modules are also presented here, notably for tilting, cotilting, Baer, and Mittag-Leffler modules. In the second volume, Predictions, further basic instruments are introduced: the prediction principles, and their applications to proving realization theorems. Moreover, tools are developed there for answering problems motivated in algebraic topology. The authors concentrate on the impossibility of classification for modules over general rings. The wild character of many categories C of modules is documented here by the realization theorems that represent critical R-algebras over commutative rings R as endomorphism algebras of modules from C. The monograph starts from basic facts and gradually develops the theory towards its present frontiers. It is suitable both for graduate students interested in algebra and for experts in module and representation theory.
Book Synopsis Commutative Algebra, Algebraic Geometry, and Computational Methods by : David Eisenbud
Download or read book Commutative Algebra, Algebraic Geometry, and Computational Methods written by David Eisenbud and published by Springer. This book was released on 1999-07 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains papers presented at the International Conference on Commutative Algebra, Algebraic geometry, and Computational methods held in Hanoi in 1996, as well as papers written subsequently. It features both expository articles as well as research papers on a range of currently active areas in commutative algebra, algebraic geometry (particularly surveys on intersection theory) and combinatorics. In addition, a special feature is a section on the life and work of Wolfgang Vogel, who was an organiser of the conference.
Book Synopsis Commutative Algebra - Proceedings Of The Workshop by : Giuseppe Valla
Download or read book Commutative Algebra - Proceedings Of The Workshop written by Giuseppe Valla and published by World Scientific. This book was released on 1994-08-19 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: In a relatively short time, commutative algebra has grown in many directions. Over a period of nearly fifty years starting from the so-called homological period till today, the area has developed into a rich laboratory of methods, structures and problem-solving tools.One could say a distinct modern trend of commutative algebra is a strong interaction with various aspects of Combinatorics and Computer Algebra. This has resulted in a new sense of measuring for old assumptions, and a better understanding of old results.At the same time, Invariant Theory and Algebraic Geometry remain constituents of an everlasting classical source, responsible for important themes that have been developed in Commutative Algebra — such as deformation, linkage, algebraic tori and determinantal rings, etc.This volume of proceedings is well-entrenched on the lines of development outlined above. As such, it aims to keep researchers and mathematicians well-informed of the developments in the field.
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.
Book Synopsis Commutative Algebra by : Marco Fontana
Download or read book Commutative Algebra written by Marco Fontana and published by Springer. This book was released on 2014-07-15 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents a multi-dimensional collection of articles highlighting recent developments in commutative algebra. It also includes an extensive bibliography and lists a substantial number of open problems that point to future directions of research in the represented subfields. The contributions cover areas in commutative algebra that have flourished in the last few decades and are not yet well represented in book form. Highlighted topics and research methods include Noetherian and non- Noetherian ring theory as well as integer-valued polynomials and functions. Specific topics include: · Homological dimensions of Prüfer-like rings · Quasi complete rings · Total graphs of rings · Properties of prime ideals over various rings · Bases for integer-valued polynomials · Boolean subrings · The portable property of domains · Probabilistic topics in Intn(D) · Closure operations in Zariski-Riemann spaces of valuation domains · Stability of domains · Non-Noetherian grade · Homotopy in integer-valued polynomials · Localizations of global properties of rings · Topics in integral closure · Monoids and submonoids of domains The book includes twenty articles written by many of the most prominent researchers in the field. Most contributions are authored by attendees of the conference in commutative algebra held at the Graz University of Technology in December 2012. There is also a small collection of invited articles authored by those who did not attend the conference. Following the model of the Graz conference, the volume contains a number of comprehensive survey articles along with related research articles featuring recent results that have not yet been published elsewhere.
Book Synopsis Undergraduate Commutative Algebra by : Miles Reid
Download or read book Undergraduate Commutative Algebra written by Miles Reid and published by Cambridge University Press. This book was released on 1995-11-30 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: Commutative algebra is at the crossroads of algebra, number theory and algebraic geometry. This textbook is affordable and clearly illustrated, and is intended for advanced undergraduate or beginning graduate students with some previous experience of rings and fields. Alongside standard algebraic notions such as generators of modules and the ascending chain condition, the book develops in detail the geometric view of a commutative ring as the ring of functions on a space. The starting point is the Nullstellensatz, which provides a close link between the geometry of a variety V and the algebra of its coordinate ring A=k[V]; however, many of the geometric ideas arising from varieties apply also to fairly general rings. The final chapter relates the material of the book to more advanced topics in commutative algebra and algebraic geometry. It includes an account of some famous 'pathological' examples of Akizuki and Nagata, and a brief but thought-provoking essay on the changing position of abstract algebra in today's world.
