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Author: Hans Schoutens
Publisher: Springer Science & Business Media
Published: 2010-07-31
Total Pages: 215
ISBN-13: 3642133673
DOWNLOAD EBOOKExploring ultraproducts of Noetherian local rings from an algebraic perspective, this volume illustrates the many ways they can be used in commutative algebra. The text includes an introduction to tight closure in characteristic zero, a survey of flatness criteria, and more.
Author: James A. Nickerson
Publisher:
Published: 1983
Total Pages: 110
ISBN-13:
DOWNLOAD EBOOKAuthor: Marco Fontana
Publisher: Springer Science & Business Media
Published: 2010-09-29
Total Pages: 491
ISBN-13: 144196990X
DOWNLOAD EBOOKCommutative algebra is a rapidly growing subject that is developing in many different directions. This volume presents several of the most recent results from various areas related to both Noetherian and non-Noetherian commutative algebra. This volume contains a collection of invited survey articles by some of the leading experts in the field. The authors of these chapters have been carefully selected for their important contributions to an area of commutative-algebraic research. Some topics presented in the volume include: generalizations of cyclic modules, zero divisor graphs, class semigroups, forcing algebras, syzygy bundles, tight closure, Gorenstein dimensions, tensor products of algebras over fields, as well as many others. This book is intended for researchers and graduate students interested in studying the many topics related to commutative algebra.
Author: Huishi Li
Publisher: World Scientific
Published: 2004
Total Pages: 198
ISBN-13: 9789812389510
DOWNLOAD EBOOK- Contains many examples and problems (with hints) - Provides a good introduction for beginners in algebraic number theory and algebraic geometry
Author: James Thomson Knight
Publisher: Cambridge University Press
Published: 1971-10-31
Total Pages: 141
ISBN-13: 0521081939
DOWNLOAD EBOOKThis 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.
Author: Irena Peeva
Publisher: Springer Science & Business Media
Published: 2013-02-01
Total Pages: 705
ISBN-13: 1461452929
DOWNLOAD EBOOKThis 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.
Author: J. William Hoffman
Publisher: Mercury Learning and Information
Published: 2016-04-15
Total Pages: 220
ISBN-13: 1944534709
DOWNLOAD EBOOKThe 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.
Author: Andrea Ferretti
Publisher: American Mathematical Society
Published: 2023-09-26
Total Pages: 394
ISBN-13: 1470471272
DOWNLOAD EBOOKThis book provides an introduction to classical methods in commutative algebra and their applications to number theory, algebraic geometry, and computational algebra. The use of number theory as a motivating theme throughout the book provides a rich and interesting context for the material covered. In addition, many results are reinterpreted from a geometric perspective, providing further insight and motivation for the study of commutative algebra. The content covers the classical theory of Noetherian rings, including primary decomposition and dimension theory, topological methods such as completions, computational techniques, local methods and multiplicity theory, as well as some topics of a more arithmetic nature, including the theory of Dedekind rings, lattice embeddings, and Witt vectors. Homological methods appear in the author's sequel, Homological Methods in Commutative Algebra. Overall, this book is an excellent resource for advanced undergraduates and beginning graduate students in algebra or number theory. It is also suitable for students in neighboring fields such as algebraic geometry who wish to develop a strong foundation in commutative algebra. Some parts of the book may be useful to supplement undergraduate courses in number theory, computational algebra or algebraic geometry. The clear and detailed presentation, the inclusion of computational techniques and arithmetic topics, and the numerous exercises make it a valuable addition to any library.
Author: Ernst Kunz
Publisher: Springer Science & Business Media
Published: 2012-11-06
Total Pages: 253
ISBN-13: 1461459877
DOWNLOAD EBOOKOriginally 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.
Author: Marco Fontana
Publisher: Walter de Gruyter
Published: 2009
Total Pages: 395
ISBN-13: 311020746X
DOWNLOAD EBOOKThis volume contains selected refereed papers based on lectures presented at the 'Fifth International Fez Conference on Commutative Algebra and Applications' that was held in Fez, Morocco in June 2008. The volume represents new trends and areas of classical research within the field, with contributions from many different countries. In addition, the volume has as a special focus the research and influence of Alain Bouvier on commutative algebra over the past thirty years.
