Topics In Commutative Ring Theory PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Topics In Commutative Ring Theory PDF full book. Access full book title Topics In Commutative Ring Theory.
Author | : John J. Watkins |
Publisher | : Princeton University Press |
Total Pages | : 228 |
Release | : 2009-02-09 |
Genre | : Mathematics |
ISBN | : 1400828171 |
Download Topics in Commutative Ring Theory Book in PDF, ePub and Kindle
Topics in Commutative Ring Theory is a textbook for advanced undergraduate students as well as graduate students and mathematicians seeking an accessible introduction to this fascinating area of abstract algebra. Commutative ring theory arose more than a century ago to address questions in geometry and number theory. A commutative ring is a set-such as the integers, complex numbers, or polynomials with real coefficients--with two operations, addition and multiplication. Starting from this simple definition, John Watkins guides readers from basic concepts to Noetherian rings-one of the most important classes of commutative rings--and beyond to the frontiers of current research in the field. Each chapter includes problems that encourage active reading--routine exercises as well as problems that build technical skills and reinforce new concepts. The final chapter is devoted to new computational techniques now available through computers. Careful to avoid intimidating theorems and proofs whenever possible, Watkins emphasizes the historical roots of the subject, like the role of commutative rings in Fermat's last theorem. He leads readers into unexpected territory with discussions on rings of continuous functions and the set-theoretic foundations of mathematics. Written by an award-winning teacher, this is the first introductory textbook to require no prior knowledge of ring theory to get started. Refreshingly informal without ever sacrificing mathematical rigor, Topics in Commutative Ring Theory is an ideal resource for anyone seeking entry into this stimulating field of study.
Author | : Hideyuki Matsumura |
Publisher | : Cambridge University Press |
Total Pages | : 338 |
Release | : 1989-05-25 |
Genre | : Mathematics |
ISBN | : 9780521367646 |
Download Commutative Ring Theory Book in PDF, ePub and Kindle
This book explores commutative ring theory, an important a foundation for algebraic geometry and complex analytical geometry.
Author | : Fanggui Wang |
Publisher | : Springer |
Total Pages | : 714 |
Release | : 2017-01-06 |
Genre | : Mathematics |
ISBN | : 9811033374 |
Download Foundations of Commutative Rings and Their Modules Book in PDF, ePub and Kindle
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.
Author | : I. N. Herstein |
Publisher | : |
Total Pages | : 156 |
Release | : 1969 |
Genre | : Mathematics |
ISBN | : |
Download Topics in Ring Theory Book in PDF, ePub and Kindle
Author | : Michael F. Atiyah |
Publisher | : CRC Press |
Total Pages | : 140 |
Release | : 2018-03-09 |
Genre | : Mathematics |
ISBN | : 0429973268 |
Download Introduction To Commutative Algebra Book in PDF, ePub and Kindle
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.
Author | : S.T. Chapman |
Publisher | : Springer Science & Business Media |
Total Pages | : 477 |
Release | : 2013-03-09 |
Genre | : Mathematics |
ISBN | : 1475731809 |
Download Non-Noetherian Commutative Ring Theory Book in PDF, ePub and Kindle
Commutative Ring Theory emerged as a distinct field of research in math ematics only at the beginning of the twentieth century. It is rooted in nine teenth century major works in Number Theory and Algebraic Geometry for which it provided a useful tool for proving results. From this humble origin, it flourished into a field of study in its own right of an astonishing richness and interest. Nowadays, one has to specialize in an area of this vast field in order to be able to master its wealth of results and come up with worthwhile contributions. One of the major areas of the field of Commutative Ring Theory is the study of non-Noetherian rings. The last ten years have seen a lively flurry of activity in this area, including: a large number of conferences and special sections at national and international meetings dedicated to presenting its results, an abundance of articles in scientific journals, and a substantial number of books capturing some of its topics. This rapid growth, and the occasion of the new Millennium, prompted us to embark on a project aimed at presenting an overview of the recent research in the area. With this in mind, we invited many of the most prominent researchers in Non-Noetherian Commutative Ring Theory to write expository articles representing the most recent topics of research in this area.
Author | : Alfred Geroldinger |
Publisher | : CRC Press |
Total Pages | : 723 |
Release | : 2006-01-13 |
Genre | : Mathematics |
ISBN | : 1420003208 |
Download Non-Unique Factorizations Book in PDF, ePub and Kindle
From its origins in algebraic number theory, the theory of non-unique factorizations has emerged as an independent branch of algebra and number theory. Focused efforts over the past few decades have wrought a great number and variety of results. However, these remain dispersed throughout the vast literature. For the first time, Non-Unique Factoriza
Author | : David Dobbs |
Publisher | : CRC Press |
Total Pages | : 578 |
Release | : 2023-08-25 |
Genre | : Mathematics |
ISBN | : 1000939634 |
Download Advances in Commutative Ring Theory Book in PDF, ePub and Kindle
"Presents the proceedings of the recently held Third International Conference on Commutative Ring Theory in Fez, Morocco. Details the latest developments in commutative algebra and related areas-featuring 26 original research articles and six survey articles on fundamental topics of current interest. Examines wide-ranging developments in commutative algebra, together with connections to algebraic number theory and algebraic geometry."
Author | : Gert-Martin Greuel |
Publisher | : Springer Science & Business Media |
Total Pages | : 601 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 3662049635 |
Download A Singular Introduction to Commutative Algebra Book in PDF, ePub and Kindle
This book can be understood as a model for teaching commutative algebra, and takes into account modern developments such as algorithmic and computational aspects. As soon as a new concept is introduced, the authors show how the concept can be worked on using a computer. The computations are exemplified with the computer algebra system Singular, developed by the authors. Singular is a special system for polynomial computation with many features for global as well as for local commutative algebra and algebraic geometry. The book includes a CD containing Singular as well as the examples and procedures explained in the book.
Author | : Ernst Kunz |
Publisher | : Springer Science & Business Media |
Total Pages | : 253 |
Release | : 2012-11-06 |
Genre | : Mathematics |
ISBN | : 1461459877 |
Download Introduction to Commutative Algebra and Algebraic Geometry Book in PDF, ePub and Kindle
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.