An Introduction to Module 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 An Introduction to Module Theory PDF full book. Access full book title An Introduction to Module Theory by Ibrahim Assem. Download full books in PDF and EPUB format.
Author: Ibrahim Assem
Publisher: Oxford University Press
ISBN: 0198904924
Category : Mathematics
Languages : en
Pages : 609
Get Book Here
Book Description
Module theory is a fundamental area of algebra, taught in most universities at the graduate level. This textbook, written by two experienced teachers and researchers in the area, is based on courses given in their respective universities over the last thirty years. It is an accessible and modern account of module theory, meant as a textbook for graduate or advanced undergraduate students, though it can also be used for self-study. It is aimed at students in algebra, or students who need algebraic tools in their work. Following the recent trends in the area, the general approach stresses from the start the use of categorical and homological techniques. The book includes self-contained introductions to category theory and homological algebra with applications to Module theory, and also contains an introduction to representations of quivers. It includes a very large number of examples of all kinds worked out in detail, mostly of abelian groups, modules over matrix algebras, polynomial algebras, or algebras given by bound quivers. In order to help visualise and analyse examples, it includes many figures. Each section is followed by exercises of all levels of difficulty, both computational and theoretical, with hints provided to some of them.
Author: Lars W. Christensen
Publisher: Springer
ISBN: 3540400087
Category : Mathematics
Languages : en
Pages : 209
Get Book Here
Book Description
This book is intended as a reference for mathematicians working with homological dimensions in commutative algebra and as an introduction to Gorenstein dimensions for graduate students with an interest in the same. Any admirer of classics like the Auslander-Buchsbaum-Serre characterization of regular rings, and the Bass and Auslander-Buchsbaum formulas for injective and projective dimension of f.g. modules will be intrigued by this book's content. Readers should be well-versed in commutative algebra and standard applications of homological methods. The framework is that of complexes, but all major results are restated for modules in traditional notation, and an appendix makes the proofs accessible for even the casual user of hyperhomological methods.
Author: T.Y. Lam
Publisher: Springer Science & Business Media
ISBN: 0387488995
Category : Mathematics
Languages : en
Pages : 427
Get Book Here
Book Description
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: Ibrahim Assem
Publisher: Oxford University Press
ISBN: 0198904924
Category : Mathematics
Languages : en
Pages : 609
Get Book Here
Book Description
Module theory is a fundamental area of algebra, taught in most universities at the graduate level. This textbook, written by two experienced teachers and researchers in the area, is based on courses given in their respective universities over the last thirty years. It is an accessible and modern account of module theory, meant as a textbook for graduate or advanced undergraduate students, though it can also be used for self-study. It is aimed at students in algebra, or students who need algebraic tools in their work. Following the recent trends in the area, the general approach stresses from the start the use of categorical and homological techniques. The book includes self-contained introductions to category theory and homological algebra with applications to Module theory, and also contains an introduction to representations of quivers. It includes a very large number of examples of all kinds worked out in detail, mostly of abelian groups, modules over matrix algebras, polynomial algebras, or algebras given by bound quivers. In order to help visualise and analyse examples, it includes many figures. Each section is followed by exercises of all levels of difficulty, both computational and theoretical, with hints provided to some of them.
Author: Tsit-Yuen Lam
Publisher: Springer Science & Business Media
ISBN: 1461205255
Category : Mathematics
Languages : en
Pages : 577
Get Book Here
Book Description
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: Toma Albu
Publisher: Springer Science & Business Media
ISBN: 3034600070
Category : Mathematics
Languages : en
Pages : 204
Get Book Here
Book Description
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: Charles A. Weibel
Publisher: Cambridge University Press
ISBN: 113964307X
Category : Mathematics
Languages : en
Pages : 470
Get Book Here
Book Description
The landscape of homological algebra has evolved over the last half-century into a fundamental tool for the working mathematician. This book provides a unified account of homological algebra as it exists today. The historical connection with topology, regular local rings, and semi-simple Lie algebras are also described. This book is suitable for second or third year graduate students. The first half of the book takes as its subject the canonical topics in homological algebra: derived functors, Tor and Ext, projective dimensions and spectral sequences. Homology of group and Lie algebras illustrate these topics. Intermingled are less canonical topics, such as the derived inverse limit functor lim1, local cohomology, Galois cohomology, and affine Lie algebras. The last part of the book covers less traditional topics that are a vital part of the modern homological toolkit: simplicial methods, Hochschild and cyclic homology, derived categories and total derived functors. By making these tools more accessible, the book helps to break down the technological barrier between experts and casual users of homological algebra.
Author: Viet Dung Nguyen
Publisher: American Mathematical Soc.
ISBN: 0821843702
Category : Mathematics
Languages : en
Pages : 377
Get Book Here
Book Description
The papers in this volume contain results in active research areas in the theory of rings and modules, including non commutative and commutative ring theory, module theory, representation theory, and coding theory.
Author: Michiel Hazewinkel
Publisher: Springer Science & Business Media
ISBN: 9400959974
Category : Mathematics
Languages : en
Pages : 525
Get Book Here
Book Description
This ENCYCLOPAEDIA OF MATHEMATICS aims to be a reference work for all parts of mathe matics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977-1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fine subdivi sion has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathematics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, en gineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques.
Author: Leonid Positselski
Publisher: American Mathematical Soc.
ISBN: 0821852965
Category : Mathematics
Languages : en
Pages : 146
Get Book Here
Book Description
"July 2011, volume 212, number 996 (first of 4 numbers)."
Author: Edgar E. Enochs
Publisher: Walter de Gruyter
ISBN: 3110215217
Category : Mathematics
Languages : en
Pages : 377
Get Book Here
Book Description
This is the second revised edition of an introduction to contemporary relative homological algebra. It supplies important material essential to understand topics in algebra, algebraic geometry and algebraic topology. Each section comes with exercises providing practice problems for students as well as additional important results for specialists. In this new edition the authors have added well-known additional material in the first three chapters, and added new material that was not available at the time the original edition was published. In particular, the major changes are the following: Chapter 1: Section 1.2 has been rewritten to clarify basic notions for the beginner, and this has necessitated a new Section 1.3. Chapter 3: The classic work of D. G. Northcott on injective envelopes and inverse polynomials is finally included. This provides additional examples for the reader. Chapter 11: Section 11.9 on Kaplansky classes makes volume one more up to date. The material in this section was not available at the time the first edition was published. The authors also have clarified some text throughout the book and updated the bibliography by adding new references. The book is also suitable for an introductory course in commutative and ordinary homological algebra.
