Algebras Rings And Modules PDF Download
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Author | : Michiel Hazewinkel |
Publisher | : CRC Press |
Total Pages | : 384 |
Release | : 2016-04-05 |
Genre | : Mathematics |
ISBN | : 1482245051 |
Download Algebras, Rings and Modules Book in PDF, ePub and Kindle
The theory of algebras, rings, and modules is one of the fundamental domains of modern mathematics. General algebra, more specifically non-commutative algebra, is poised for major advances in the twenty-first century (together with and in interaction with combinatorics), just as topology, analysis, and probability experienced in the twentieth centu
Author | : Frank W. Anderson |
Publisher | : Springer Science & Business Media |
Total Pages | : 386 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461244188 |
Download Rings and Categories of Modules Book in PDF, ePub and Kindle
This book is intended to provide a reasonably self-contained account of a major portion of the general theory of rings and modules suitable as a text for introductory and more advanced graduate courses. We assume the famil iarity with rings usually acquired in standard undergraduate algebra courses. Our general approach is categorical rather than arithmetical. The continuing theme of the text is the study of the relationship between the one-sided ideal structure that a ring may possess and the behavior of its categories of modules. Following a brief outline of set-theoretic and categorical foundations, the text begins with the basic definitions and properties of rings, modules and homomorphisms and ranges through comprehensive treatments of direct sums, finiteness conditions, the Wedderburn-Artin Theorem, the Jacobson radical, the hom and tensor functions, Morita equivalence and duality, de composition theory of injective and projective modules, and semi perfect and perfect rings. In this second edition we have included a chapter containing many of the classical results on artinian rings that have hdped to form the foundation for much of the contemporary research on the representation theory of artinian rings and finite dimensional algebras. Both to illustrate the text and to extend it we have included a substantial number of exercises covering a wide spectrum of difficulty. There are, of course" many important areas of ring and module theory that the text does not touch upon.
Author | : Alberto Facchini |
Publisher | : CRC Press |
Total Pages | : 530 |
Release | : 2020-02-10 |
Genre | : Mathematics |
ISBN | : 9780824750817 |
Download Rings, Modules, Algebras, and Abelian Groups Book in PDF, ePub and Kindle
Rings, Modules, Algebras, and Abelian Groups summarizes the proceedings of a recent algebraic conference held at Venice International University in Italy. Surveying the most influential developments in the field, this reference reviews the latest research on Abelian groups, algebras and their representations, module and ring theory, and topological
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 | : Craig Huneke |
Publisher | : Cambridge University Press |
Total Pages | : 446 |
Release | : 2006-10-12 |
Genre | : Mathematics |
ISBN | : 0521688604 |
Download Integral Closure of Ideals, Rings, and Modules Book in PDF, ePub and Kindle
Ideal for graduate students and researchers, this book presents a unified treatment of the central notions of integral closure.
Author | : John Dauns |
Publisher | : Cambridge University Press |
Total Pages | : 470 |
Release | : 1994-10-28 |
Genre | : Mathematics |
ISBN | : 0521462584 |
Download Modules and Rings Book in PDF, ePub and Kindle
This book on modern module and non-commutative ring theory is ideal for beginning graduate students. It starts at the foundations of the subject and progresses rapidly through the basic concepts to help the reader reach current research frontiers. Students will have the chance to develop proofs, solve problems, and to find interesting questions. The first half of the book is concerned with free, projective, and injective modules, tensor algebras, simple modules and primitive rings, the Jacobson radical, and subdirect products. Later in the book, more advanced topics, such as hereditary rings, categories and functors, flat modules, and purity are introduced. These later chapters will also prove a useful reference for researchers in non-commutative ring theory. Enough background material (including detailed proofs) is supplied to give the student a firm grounding in the subject.
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 | : William A. Adkins |
Publisher | : Springer Science & Business Media |
Total Pages | : 540 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461209234 |
Download Algebra Book in PDF, ePub and Kindle
This book is designed as a text for a first-year graduate algebra course. As necessary background we would consider a good undergraduate linear algebra course. An undergraduate abstract algebra course, while helpful, is not necessary (and so an adventurous undergraduate might learn some algebra from this book). Perhaps the principal distinguishing feature of this book is its point of view. Many textbooks tend to be encyclopedic. We have tried to write one that is thematic, with a consistent point of view. The theme, as indicated by our title, is that of modules (though our intention has not been to write a textbook purely on module theory). We begin with some group and ring theory, to set the stage, and then, in the heart of the book, develop module theory. Having developed it, we present some of its applications: canonical forms for linear transformations, bilinear forms, and group representations. Why modules? The answer is that they are a basic unifying concept in mathematics. The reader is probably already familiar with the basic role that vector spaces play in mathematics, and modules are a generaliza tion of vector spaces. (To be precise, modules are to rings as vector spaces are to fields.
Author | : Ihsen Yengui |
Publisher | : Springer |
Total Pages | : 277 |
Release | : 2015-12-11 |
Genre | : Mathematics |
ISBN | : 3319194941 |
Download Constructive Commutative Algebra Book in PDF, ePub and Kindle
The main goal of this book is to find the constructive content hidden in abstract proofs of concrete theorems in Commutative Algebra, especially in well-known theorems concerning projective modules over polynomial rings (mainly the Quillen-Suslin theorem) and syzygies of multivariate polynomials with coefficients in a valuation ring. Simple and constructive proofs of some results in the theory of projective modules over polynomial rings are also given, and light is cast upon recent progress on the Hermite ring and Gröbner ring conjectures. New conjectures on unimodular completion arising from our constructive approach to the unimodular completion problem are presented. Constructive algebra can be understood as a first preprocessing step for computer algebra that leads to the discovery of general algorithms, even if they are sometimes not efficient. From a logical point of view, the dynamical evaluation gives a constructive substitute for two highly nonconstructive tools of abstract algebra: the Law of Excluded Middle and Zorn's Lemma. For instance, these tools are required in order to construct the complete prime factorization of an ideal in a Dedekind ring, whereas the dynamical method reveals the computational content of this construction. These lecture notes follow this dynamical philosophy.