Lectures On Modules And Rings PDF Download
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Author | : Tsit-Yuen Lam |
Publisher | : Springer Science & Business Media |
Total Pages | : 577 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461205255 |
Download Lectures on Modules and Rings Book in PDF, ePub and Kindle
This new book can be read independently from the first volume and may be used for lecturing, seminar- and self-study, or for general reference. It focuses more on specific topics in order to introduce readers to a wealth of basic and useful ideas without the hindrance of heavy machinery or undue abstractions. User-friendly with its abundance of examples illustrating the theory at virtually every step, the volume contains a large number of carefully chosen exercises to provide newcomers with practice, while offering a rich additional source of information to experts. A direct approach is used in order to present the material in an efficient and economic way, thereby introducing readers to a considerable amount of interesting ring theory without being dragged through endless preparatory material.
Author | : T.Y. Lam |
Publisher | : Springer Science & Business Media |
Total Pages | : 427 |
Release | : 2009-12-08 |
Genre | : Mathematics |
ISBN | : 0387488995 |
Download Exercises in Modules and Rings Book in PDF, ePub and Kindle
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.
Author | : Joachim Lambek |
Publisher | : |
Total Pages | : 206 |
Release | : 1966 |
Genre | : Associative rings |
ISBN | : |
Download Lectures on Rings and Modules Book in PDF, ePub and Kindle
Author | : T.Y. Lam |
Publisher | : Springer Science & Business Media |
Total Pages | : 410 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1468404067 |
Download A First Course in Noncommutative Rings Book in PDF, ePub and Kindle
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.
Author | : Joachim Lambek |
Publisher | : American Mathematical Soc. |
Total Pages | : 196 |
Release | : 2009 |
Genre | : Associative rings |
ISBN | : 082184900X |
Download Lectures on Rings and Modules Book in PDF, ePub and Kindle
This book is an introduction to the theory of associative rings and their modules, designed primarily for graduate students. The standard topics on the structure of rings are covered, with a particular emphasis on the concept of the complete ring of quotients. A survey of the fundamental concepts of algebras in the first chapter helps to make the treatment self-contained. The topics covered include selected results on Boolean and other commutative rings, the classical structure theory of associative rings, injective modules, and rings of quotients. The final chapter provides an introduction to homological algebra. Besides three appendices on further results, there is a six-page section of historical comments. Table of Contents: Fundamental Concepts of Algebra: 1.1 Rings and related algebraic systems; 1.2 Subrings, homomorphisms, ideals; 1.3 Modules, direct products, and direct sums; 1.4 Classical isomorphism theorems. Selected Topics on Commutative Rings: 2.1 Prime ideals in commutative rings; 2.2 Prime ideals in special commutative rings; 2.3 The complete ring of quotients of a commutative ring; 2.4 Rings of quotients of commutative semiprime rings; 2.5 Prime ideal spaces.Classical Theory of Associative Rings: 3.1 Primitive rings; 3.2 Radicals; 3.3 Completely reducible modules; 3.4 Completely reducible rings; 3.5 Artinian and Noetherian rings; 3.6 On lifting idempotents; 3.7 Local and semiperfect rings. Injectivity and Related Concepts: 4.1 Projective modules; 4.2 Injective modules; 4.3 The complete ring of quotients; 4.4 Rings of endomorphisms of injective modules; 4.5 Regular rings of quotients; 4.6 Classical rings of quotients; 4.7 The Faith-Utumi theorem. Introduction to Homological Algebra: 5.1 Tensor products of modules; 5.2 Hom and $\otimes$ as functors; 5.3 Exact sequences; 5.4 Flat modules; 5.5 Torsion and extension products. Appendixes; Comments; Bibliography; Index. Review from Zentralblatt Math: Due to their clarity and intelligible presentation, these lectures on rings and modules are a particularly successful introduction to the surrounding circle of ideas. Review from American Mathematical Monthly: An introduction to associative rings and modules which requires of the reader only the mathematical maturity which one would attain in a first-year graduate algebra [course]...in order to make the contents of the book as accessible as possible, the author develops all the fundamentals he will need.In addition to covering the basic topics...the author covers some topics not so readily available to the nonspecialist...the chapters are written to be as independent as possible...[which will be appreciated by] students making their first acquaintance with the subject...one of the most successful features of the book is that it can be read by graduate students with little or no help from a specialist. (CHEL/283.H)
Author | : John A. Beachy |
Publisher | : Cambridge University Press |
Total Pages | : 252 |
Release | : 1999-04-22 |
Genre | : Mathematics |
ISBN | : 9780521644075 |
Download Introductory Lectures on Rings and Modules Book in PDF, ePub and Kindle
A first-year graduate text or reference for advanced undergraduates on noncommutative aspects of rings and modules.
Author | : Toma Albu |
Publisher | : Springer Science & Business Media |
Total Pages | : 204 |
Release | : 2011-02-04 |
Genre | : Mathematics |
ISBN | : 3034600070 |
Download Ring and Module Theory Book in PDF, ePub and Kindle
This book is a collection of invited papers and articles, many presented at the 2008 International Conference on Ring and Module Theory. The papers explore the latest in various areas of algebra, including ring theory, module theory and commutative algebra.
Author | : Kenneth Goodearl |
Publisher | : CRC Press |
Total Pages | : 224 |
Release | : 1976-03-01 |
Genre | : Mathematics |
ISBN | : 9780824763541 |
Download Ring Theory Book in PDF, ePub and Kindle
Author | : Shreeram Shankar Abhyankar |
Publisher | : World Scientific |
Total Pages | : 758 |
Release | : 2006 |
Genre | : Mathematics |
ISBN | : 9812568263 |
Download Lectures on Algebra Book in PDF, ePub and Kindle
This book is a timely survey of much of the algebra developed during the last several centuries including its applications to algebraic geometry and its potential use in geometric modeling. The present volume makes an ideal textbook for an abstract algebra course, while the forthcoming sequel. Lectures on Algebra II, will serve as a textbook for a linear algebra course. The author's fondness for algebraic geometry shows up in both volumes, and his recent preoccupation with the applications of group theory to the calculation of Galois groups is evident in the second volume which contains more local rings and more algebraic geometry. Both books are based on the author's lectures at Purdue University over the last few years.
Author | : Irving Kaplansky |
Publisher | : University of Chicago Press |
Total Pages | : 217 |
Release | : 1972 |
Genre | : Mathematics |
ISBN | : 0226424510 |
Download Fields and Rings Book in PDF, ePub and Kindle
This book combines in one volume Irving Kaplansky's lecture notes on the theory of fields, ring theory, and homological dimensions of rings and modules. "In all three parts of this book the author lives up to his reputation as a first-rate mathematical stylist. Throughout the work the clarity and precision of the presentation is not only a source of constant pleasure but will enable the neophyte to master the material here presented with dispatch and ease."—A. Rosenberg, Mathematical Reviews