A First Course in Rings and Ideals
Author: David M. Burton
Publisher: Addison-Wesley
Published: 1970
Total Pages: 328
ISBN-13:
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A First Course in Noncommutative Rings
Author: T.Y. Lam
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 410
ISBN-13: 1468404067
DOWNLOAD EBOOKOne 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.
A First Course in Abstract Algebra
Author: Marlow Anderson
Publisher: CRC Press
Published: 2005-01-27
Total Pages: 684
ISBN-13: 1420057111
DOWNLOAD EBOOKMost abstract algebra texts begin with groups, then proceed to rings and fields. While groups are the logically simplest of the structures, the motivation for studying groups can be somewhat lost on students approaching abstract algebra for the first time. To engage and motivate them, starting with something students know and abstracting from there
A Course in Ring Theory
Author: Donald S. Passman
Publisher: American Mathematical Soc.
Published: 2004-09-28
Total Pages: 324
ISBN-13: 9780821869383
DOWNLOAD EBOOKProjective modules: Modules and homomorphisms Projective modules Completely reducible modules Wedderburn rings Artinian rings Hereditary rings Dedekind domains Projective dimension Tensor products Local rings Polynomial rings: Skew polynomial rings Grothendieck groups Graded rings and modules Induced modules Syzygy theorem Patching theorem Serre conjecture Big projectives Generic flatness Nullstellensatz Injective modules: Injective modules Injective dimension Essential extensions Maximal ring of quotients Classical ring of quotients Goldie rings Uniform dimension Uniform injective modules Reduced rank Index
Integral Closure of Ideals, Rings, and Modules
Author: Craig Huneke
Publisher: Cambridge University Press
Published: 2006-10-12
Total Pages: 446
ISBN-13: 0521688604
DOWNLOAD EBOOKIdeal for graduate students and researchers, this book presents a unified treatment of the central notions of integral closure.
Rings and Ideals
Author: Neal H. McCoy
Publisher: American Mathematical Soc.
Published: 1948-12-31
Total Pages: 229
ISBN-13: 1614440085
DOWNLOAD EBOOKThis monograph presents an introduction to that branch of abstract algebra having to do with the theory of rings, with some emphasis on the role of ideals in the theory. Except for a knowledge of certain fundamental theorems about determinants which is assumed in Chapter VIII, and at one point in Chapter VII, the book is almost entirely self-contained. Of course, the reader must have a certain amount of “mathematical maturity” in order to understand the illustrative examples and also to grasp the significance of the abstract approach. However, as far as formal technique is concerned, little more than the elements of algebra are presupposed.
A First Course in Module Theory
Author: M. E. Keating
Publisher: World Scientific Publishing Company
Published: 1998-01-01
Total Pages: 250
ISBN-13: 9781860940965
DOWNLOAD EBOOKAn introduction to module theory for students with some knowledge of linear algebra and elementary ring theory. Expounds the basics of module theory, including methods of comparing, constructing and decomposing modules, then presents the structure theory of modules over Euclidean domains. Concluding chapters look at two standard forms for a square matrix, and projective modules over rings in general. Annotation copyrighted by Book News, Inc., Portland, OR
Algebra in Action: A Course in Groups, Rings, and Fields
Author: Shahriar Shahriar
Publisher: American Mathematical Soc.
Published: 2017-08-16
Total Pages: 698
ISBN-13: 1470428490
DOWNLOAD EBOOKThis text—based on the author's popular courses at Pomona College—provides a readable, student-friendly, and somewhat sophisticated introduction to abstract algebra. It is aimed at sophomore or junior undergraduates who are seeing the material for the first time. In addition to the usual definitions and theorems, there is ample discussion to help students build intuition and learn how to think about the abstract concepts. The book has over 1300 exercises and mini-projects of varying degrees of difficulty, and, to facilitate active learning and self-study, hints and short answers for many of the problems are provided. There are full solutions to over 100 problems in order to augment the text and to model the writing of solutions. Lattice diagrams are used throughout to visually demonstrate results and proof techniques. The book covers groups, rings, and fields. In group theory, group actions are the unifying theme and are introduced early. Ring theory is motivated by what is needed for solving Diophantine equations, and, in field theory, Galois theory and the solvability of polynomials take center stage. In each area, the text goes deep enough to demonstrate the power of abstract thinking and to convince the reader that the subject is full of unexpected results.
Ring and Module Theory
Author: Toma Albu
Publisher: Springer Science & Business Media
Published: 2011-02-04
Total Pages: 204
ISBN-13: 3034600070
DOWNLOAD EBOOKThis 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.
Exercises in Modules and Rings
Author: T.Y. Lam
Publisher: Springer Science & Business Media
Published: 2009-12-08
Total Pages: 427
ISBN-13: 0387488995
DOWNLOAD EBOOKThis 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.
