Algebras, Rings and Modules, Volume 2

Non-commutative Algebras and Rings

Author: Michiel Hazewinkel,Nadiya M. Gubareni

Publisher: CRC Press

ISBN: 1351869876

Category: Mathematics

Page: 364

View: 6298

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 century. This is the second volume of Algebras, Rings and Modules: Non-commutative Algebras and Rings by M. Hazewinkel and N. Gubarenis, a continuation stressing the more important recent results on advanced topics of the structural theory of associative algebras, rings and modules.

Algebras, Rings and Modules

Author: Michiel Hazewinkel,Nadiya Gubareni,V.V. Kirichenko

Publisher: Springer Science & Business Media

ISBN: 1402026919

Category: Mathematics

Page: 380

View: 7808

Accosiative rings and algebras are very interesting algebraic structures. In a strict sense, the theory of algebras (in particular, noncommutative algebras) originated fromasingleexample,namelythequaternions,createdbySirWilliamR.Hamilton in1843. Thiswasthe?rstexampleofanoncommutative”numbersystem”. During thenextfortyyearsmathematiciansintroducedotherexamplesofnoncommutative algebras, began to bring some order into them and to single out certain types of algebras for special attention. Thus, low-dimensional algebras, division algebras, and commutative algebras, were classi?ed and characterized. The ?rst complete results in the structure theory of associative algebras over the real and complex ?elds were obtained by T.Molien, E.Cartan and G.Frobenius. Modern ring theory began when J.H.Wedderburn proved his celebrated cl- si?cation theorem for ?nite dimensional semisimple algebras over arbitrary ?elds. Twenty years later, E.Artin proved a structure theorem for rings satisfying both the ascending and descending chain condition which generalized Wedderburn structure theorem. The Wedderburn-Artin theorem has since become a corn- stone of noncommutative ring theory. The purpose of this book is to introduce the subject of the structure theory of associative rings. This book is addressed to a reader who wishes to learn this topic from the beginning to research level. We have tried to write a self-contained book which is intended to be a modern textbook on the structure theory of associative rings and related structures and will be accessible for independent study.

Topics in Hyperplane Arrangements

Author: Marcelo Aguiar,Swapneel Mahajan

Publisher: American Mathematical Soc.

ISBN: 1470437112

Category: Algebraic spaces

Page: 611

View: 2321

This monograph studies the interplay between various algebraic, geometric and combinatorial aspects of real hyperplane arrangements. It provides a careful, organized and unified treatment of several recent developments in the field, and brings forth many new ideas and results. It has two parts, each divided into eight chapters, and five appendices with background material. Part I gives a detailed discussion on faces, flats, chambers, cones, gallery intervals, lunes and other geometric notions associated with arrangements. The Tits monoid plays a central role. Another important object is the category of lunes which generalizes the classical associative operad. Also discussed are the descent and lune identities, distance functions on chambers, and the combinatorics of the braid arrangement and related examples. Part II studies the structure and representation theory of the Tits algebra of an arrangement. It gives a detailed analysis of idempotents and Peirce decompositions, and connects them to the classical theory of Eulerian idempotents. It introduces the space of Lie elements of an arrangement which generalizes the classical Lie operad. This space is the last nonzero power of the radical of the Tits algebra. It is also the socle of the left ideal of chambers and of the right ideal of Zie elements. Zie elements generalize the classical Lie idempotents. They include Dynkin elements associated to generic half-spaces which generalize the classical Dynkin idempotent. Another important object is the lune-incidence algebra which marks the beginning of noncommutative Möbius theory. These ideas are also brought upon the study of the Solomon descent algebra. The monograph is written with clarity and in sufficient detail to make it accessible to graduate students. It can also serve as a useful reference to experts.

Abstract Algebra with Applications

Volume 2: Rings and Fields

Author: Karlheinz Spindler

Publisher: CRC Press

ISBN: 9780824791599

Category: Mathematics

Page: 552

View: 6776

A comprehensive presentation of abstract algebra and an in-depth treatment of the applications of algebraic techniques and the relationship of algebra to other disciplines, such as number theory, combinatorics, geometry, topology, differential equations, and Markov chains.

Approximations and Endomorphism Algebras of Modules

Volume 1 – Approximations / Volume 2 – Predictions

Author: Rüdiger Göbel,Jan Trlifaj

Publisher: Walter de Gruyter

ISBN: 3110218119

Category: Mathematics

Page: 1024

View: 3642

This monograph – now in its second revised and extended edition – provides a thorough treatment of module theory, a subfield of algebra. The authors develop an approximation theory as well as realization theorems and present some of its recent applications, notably to infinite-dimensional combinatorics and model theory. The book starts from basic facts and gradually develops the theory towards its present frontiers.

Basic Algebra

Groups, Rings and Fields

Author: P.M. Cohn

Publisher: Springer Science & Business Media

ISBN: 0857294288

Category: Mathematics

Page: 465

View: 3310

This is the first volume of a revised edition of P.M. Cohn's classic three-volume text Algebra, widely regarded as one of the most outstanding introductory algebra textbooks. This volume covers the important results of algebra. Readers should have some knowledge of linear algebra, groups and fields, although all the essential facts and definitions are recalled.

Kategorien und Funktoren

Author: Bodo Pareigis

Publisher: N.A

ISBN: N.A

Category: Categories (Mathematics)

Page: 192

View: 6254

Extensions of Rings and Modules

Author: Gary F. Birkenmeier,Jae Keol Park,S Tariq Rizvi

Publisher: Springer Science & Business Media

ISBN: 0387927166

Category: Mathematics

Page: 432

View: 1785

The "extensions" of rings and modules have yet to be explored in detail in a research monograph. This book presents state of the art research and also stimulating new and further research. Broken into three parts, Part I begins with basic notions, terminology, definitions and a description of the classes of rings and modules. Part II considers the transference of conditions between a base ring or module and its extensions. And Part III utilizes the concept of a minimal essental extension with respect to a specific class (a hull). Mathematical interdisciplinary applications appear throughout. Major applications of the ring and module theory to Functional Analysis, especially C*-algebras, appear in Part III, make this book of interest to Algebra and Functional Analysis researchers. Notes and exercises at the end of every chapter, and open problems at the end of all three parts, lend this as an ideal textbook for graduate or advanced undergradate students.

Commutative Algebra II

Author: O. Zariski,P. Samuel

Publisher: Springer Science & Business Media

ISBN: 9780387901718

Category: Mathematics

Page: 416

View: 6860

From the Preface: "topics are: (a) valuation theory; (b) theory of polynomial and power series rings (including generalizations to graded rings and modules); (c) local algebra... the algebro-geometric connections and applications of the purely algebraic material are constantly stressed and abundantly scattered throughout the exposition. Thus, this volume can be used in part as an introduction to some basic concepts and the arithmetic foundations of algebraic geometry."

Model Theoretic Algebra With Particular Emphasis on Fields, Rings, Modules

Author: Christian. U Jensen,Helmt Lenzing

Publisher: CRC Press

ISBN: 9782881247170

Category: Mathematics

Page: 464

View: 8353

Looks like a text (and a handsome one at that), but the authors prefer to describe their creation as "notes", intended to acquaint graduate students with "the power of the most basic principles of model theory by applying them to classical questions in algebra". Thirteen chapters (the last given to the enumeration of some open problems), plus tables and several appendices, bibliography. (NW) Annotation copyrighted by Book News, Inc., Portland, OR

Introductory Lectures on Rings and Modules

Author: John A. Beachy

Publisher: Cambridge University Press

ISBN: 9780521644075

Category: Mathematics

Page: 238

View: 725

A first-year graduate text or reference for advanced undergraduates on noncommutative aspects of rings and modules.

Integration and Probability

Author: Paul Malliavin

Publisher: Springer Science & Business Media

ISBN: 1461242029

Category: Mathematics

Page: 326

View: 8181

An introduction to analysis with the right mix of abstract theories and concrete problems. Starting with general measure theory, the book goes on to treat Borel and Radon measures and introduces the reader to Fourier analysis in Euclidean spaces with a treatment of Sobolev spaces, distributions, and the corresponding Fourier analysis. It continues with a Hilbertian treatment of the basic laws of probability including Doob's martingale convergence theorem and finishes with Malliavin's "stochastic calculus of variations" developed in the context of Gaussian measure spaces. This invaluable contribution gives a taste of the fact that analysis is not a collection of independent theories, but can be treated as a whole.

Algebraic K-Theory and Its Applications

Author: Jonathan Rosenberg

Publisher: Springer Science & Business Media

ISBN: 9780387942483

Category: Mathematics

Page: 394

View: 6367

Algebraic K-Theory is crucial in many areas of modern mathematics, especially algebraic topology, number theory, algebraic geometry, and operator theory. This text is designed to help graduate students in other areas learn the basics of K-Theory and get a feel for its many applications. Topics include algebraic topology, homological algebra, algebraic number theory, and an introduction to cyclic homology and its interrelationship with K-Theory.

Problems and Theorems in Analysis II

Theory of Functions. Zeros. Polynomials. Determinants. Number Theory. Geometry

Author: George Polya,Gabor Szegö

Publisher: Springer Science & Business Media

ISBN: 9783540636861

Category: Mathematics

Page: 392

View: 9338

Few mathematical books are worth translating 50 years after original publication. Polyá-Szegö is one! It was published in German in 1924, and its English edition was widely acclaimed when it appeared in 1972. In the past, more of the leading mathematicians proposed and solved problems than today. Their collection of the best in analysis is a heritage of lasting value.

commutative ring theory

Proceedings of the Ii International Conference

Author: Paul-Jean Cahen,Marco Fontana,Evan Houston,Salah-Eddine Kabbaj

Publisher: CRC Press

ISBN: 9780824798154

Category: Mathematics

Page: 488

View: 6749

Presents the proceedings of the Second International Conference on Commutative Ring Theory in Fes, Morocco. The text details developments in commutative algebra, highlighting the theory of rings and ideals. It explores commutative algebra's connections with and applications to topological algebra and algebraic geometry.

Groups, Rings, Lie and Hopf Algebras

Author: I︠U︡. A. Bakhturin

Publisher: Springer Science & Business Media

ISBN: 9781402012204

Category: Mathematics

Page: 241

View: 7895

The volume is almost entirely composed of the research and expository papers by the participants of the International Workshop "Groups, Rings, Lie and Hopf Algebras", which was held at the Memorial University of Newfoundland, St. John's, NF, Canada. All four areas from the title of the workshop are covered. In addition, some chapters touch upon the topics, which belong to two or more areas at the same time. Audience: The readership targeted includes researchers, graduate and senior undergraduate students in mathematics and its applications.

Commutative Algebra and its Applications

Proceedings of the Fifth International Fez Conference on Commutative Algebra and Applications, Fez, Morocco, June 23–28, 2008

Author: Marco Fontana,Salah-Eddine Kabbaj,Bruce Olberding,Irena Swanson

Publisher: Walter de Gruyter

ISBN: 3110213184

Category: Mathematics

Page: 394

View: 2436