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: 4347

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: 1402051417

Category: Mathematics

Page: 400

View: 6540

This second volume of this text covers the classical aspects of the theory of groups and their representations. It also offers a general introduction to the modern theory of representations including the representations of quivers and finite partially ordered sets and their applications to finite dimensional algebras. It reviews key recent developments in the theory of special ring classes including Frobenius, quasi-Frobenius, and others.

Topics in Hyperplane Arrangements

Author: Marcelo Aguiar,Swapneel Mahajan

Publisher: American Mathematical Soc.

ISBN: 1470437112

Category: Algebraic spaces

Page: 611

View: 3356

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: 400

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.

Basic Algebra

Groups, Rings and Fields

Author: P.M. Cohn

Publisher: Springer Science & Business Media

ISBN: 0857294288

Category: Mathematics

Page: 465

View: 2434

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.

Moduln und Ringe

Author: N.A

Publisher: Springer-Verlag

ISBN: 3663057038

Category: Technology & Engineering

Page: 328

View: 9872

Integration and Probability

Author: Paul Malliavin

Publisher: Springer Science & Business Media

ISBN: 1461242029

Category: Mathematics

Page: 326

View: 925

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.

Algebras and Modules Two

Author: Idun Reiten,Sverre O. Smalø,Øyvind Solberg,Canadian Mathematical Society

Publisher: American Mathematical Soc.

ISBN: 9780821810767

Category: Mathematics

Page: 569

View: 1877

This volume contains 43 research papers based on results presented at the Eighth International Conference on Representations of Algebras (ICRA VIII) held in Geiranger, Norway, in 1996. The papers, written by experts in the field, cover the most recent developments in the representation theory of artin algebras and related topics. The papers cover: representation of tame, biserial, cellular, factorial hereditary, Hopf, Koszul, non-polynomial growth, preprojective, Temperley-Lieb, tilted and quasitilted algebras. Other topics include: tilting/cotilting modules and generalizations as $*$-modules, exceptional sequences of modules and vector bundles, homological conjectures, Hochschild cohomology, cyclic homology, homologically finite subcategories, representations of posets, regular modules, vector space categories, triangulated categories, moduli spaces of representations of quivers, postprojective (and preprojective) partitions, stable and derived equivalences, and pure-injective, infinite dimensional, and endofinite representations. A general background in noncommutative algebra including rings, modules, and homological algebra is required. Features: a unique source for the developments in the representation theory of finite dimensional and artin algebras and related topics a wide variety of important papers by leading researchers in the field, with references to earlier developments in the field

Groups, Algebras, and Applications

XVIII Latin American Algebra Colloquium, August 3-8, 2009, São Pedro, Brazil

Author: César Polcino Milies

Publisher: American Mathematical Soc.

ISBN: 0821852396

Category: Mathematics

Page: 324

View: 8092

This book contains the proceedings of the XVIII Latin American Algebra Colloquium, held from August 3-8, 2009, in Sao Paulo, Brazil. It includes research articles as well as up-to-date surveys covering several directions of current research in algebra, such as Asymptotic Codimension Growth, Hopf Algebras, Structure Theory of both Associative and Non-Associative Algebras, Partial Actions of Groups on Rings, and contributions to Coding 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: 1756

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.

Linear Theory of Colombeau Generalized Functions

Author: M Nedeljkov,S Pilipovic,D Scarpalezos

Publisher: CRC Press

ISBN: 9780582356832

Category: Mathematics

Page: 168

View: 6601

Results from the now-classical distribution theory involving convolution and Fourier transformation are extended to cater for Colombeau's generalized functions. Indications are given how these particular generalized functions can be used to investigate linear equations and pseudo differential operators. Furthermore, applications are also given to problems with nonregular data.

Variational Methods in Lorentzian Geometry

Author: Antonio Masiello

Publisher: CRC Press

ISBN: 9780582237995

Category: Mathematics

Page: 200

View: 7921

Appliies variational methods and critical point theory on infinite dimenstional manifolds to some problems in Lorentzian geometry which have a variational nature, such as existence and multiplicity results on geodesics and relations between such geodesics and the topology of the manifold.

Field Theory

Author: Steven Roman

Publisher: Springer Science & Business Media

ISBN: 0387276785

Category: Mathematics

Page: 335

View: 2238

"Springer has just released the second edition of Steven Roman’s Field Theory, and it continues to be one of the best graduate-level introductions to the subject out there....Every section of the book has a number of good exercises that would make this book excellent to use either as a textbook or to learn the material on your own. All in all...a well-written expository account of a very exciting area in mathematics." --THE MAA MATHEMATICAL SCIENCES DIGITAL LIBRARY

Algebraic Topology

A First Course

Author: William Fulton

Publisher: Springer Science & Business Media

ISBN: 1461241804

Category: Mathematics

Page: 430

View: 6903

To the Teacher. This book is designed to introduce a student to some of the important ideas of algebraic topology by emphasizing the re lations of these ideas with other areas of mathematics. Rather than choosing one point of view of modem topology (homotopy theory, simplicial complexes, singular theory, axiomatic homology, differ ential topology, etc.), we concentrate our attention on concrete prob lems in low dimensions, introducing only as much algebraic machin ery as necessary for the problems we meet. This makes it possible to see a wider variety of important features of the subject than is usual in a beginning text. The book is designed for students of mathematics or science who are not aiming to become practicing algebraic topol ogists-without, we hope, discouraging budding topologists. We also feel that this approach is in better harmony with the historical devel opment of the subject. What would we like a student to know after a first course in to pology (assuming we reject the answer: half of what one would like the student to know after a second course in topology)? Our answers to this have guided the choice of material, which includes: under standing the relation between homology and integration, first on plane domains, later on Riemann surfaces and in higher dimensions; wind ing numbers and degrees of mappings, fixed-point theorems; appli cations such as the Jordan curve theorem, invariance of domain; in dices of vector fields and Euler characteristics; fundamental groups

Solution Sets of Differential Equations in Abstract Spaces

Author: Robert Dragoni,Paolo Nistri,Pietro Zecca,Jack W Macki

Publisher: CRC Press

ISBN: 9780582294509

Category: Mathematics

Page: 120

View: 7751

This book presents results on the geometric/topological structure of the solution set S of an initial-value problem x(t) = f(t, x(t)), x(0) =xo, when f is a continuous function with values in an infinite-dimensional space. A comprehensive survey of existence results and the properties of S, e.g. when S is a connected set, a retract, an acyclic set, is presented. The authors also survey results onthe properties of S for initial-value problems involving differential inclusions, and for boundary-value problems. This book will be of particular interest to researchers in ordinary and partial differential equations and some workers in control theory.

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: 7198

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.

Additive Number Theory: Inverse Problems and the Geometry of Sumsets

Author: Melvyn B. Nathanson

Publisher: Springer Science & Business Media

ISBN: 9780387946559

Category: Mathematics

Page: 296

View: 8014

Many classical problems in additive number theory are direct problems, in which one starts with a set A of natural numbers and an integer H -> 2, and tries to describe the structure of the sumset hA consisting of all sums of h elements of A. By contrast, in an inverse problem, one starts with a sumset hA, and attempts to describe the structure of the underlying set A. In recent years there has been ramrkable progress in the study of inverse problems for finite sets of integers. In particular, there are important and beautiful inverse theorems due to Freiman, Kneser, Plünnecke, Vosper, and others. This volume includes their results, and culminates with an elegant proof by Ruzsa of the deep theorem of Freiman that a finite set of integers with a small sumset must be a large subset of an n-dimensional arithmetic progression.