Abstract

This textbook, set for a one or two semester course in commutative algebra, provides an introduction to commutative algebra at the postgraduate and research levels. The main prerequisites are familiarity with groups, rings and fields. Proofs are...

Recent developments in various algebraic structures and the applications of those in different areas play an important role in Science and Technology. One of the best tools to study the non-linear algebraic systems is the theory of Near-rings.The forward...

This textbook, set for a one or two semester course in commutative algebra, provides an introduction to commutative algebra at the postgraduate and research levels. The main prerequisites are familiarity with groups, rings and fields. Proofs are...

This textbook provides an introduction to abstract algebra for advanced undergraduate students. Based on the authors' lecture notes at the Department of Mathematics, National Chung Cheng University of Taiwan, it begins with a description of the algebraic...

This textbook provides an introduction to abstract algebra for advanced undergraduate students. Based on the authors' notes at the Department of Mathematics, National Chung Cheng University, it contains material sufficient for three semesters of study...

This book provides an exposition of function field arithmetic with emphasis on recent developments concerning Drinfeld modules, the arithmetic of special values of transcendental functions (such as zeta and gamma functions and their interpolations),...

'I like the authors' taste in footnotes, what with their frequent emphasis on history, i.e. the minutiae of the lives of many mathematicians appearing in these pages. Their remarks add a particular dimension of fun and pleasure to what I think is a very...

'I like the authors' taste in footnotes, what with their frequent emphasis on history, i.e. the minutiae of the lives of many mathematicians appearing in these pages. Their remarks add a particular dimension of fun and pleasure to what I think is a very...

'I like the authors' taste in footnotes, what with their frequent emphasis on history, i.e. the minutiae of the lives of many mathematicians appearing in these pages. Their remarks add a particular dimension of fun and pleasure to what I think is a very...

'I like the authors' taste in footnotes, what with their frequent emphasis on history, i.e. the minutiae of the lives of many mathematicians appearing in these pages. Their remarks add a particular dimension of fun and pleasure to what I think is a very...

This book is mainly intended for first-year University students who undertake a basic abstract algebra course, as well as instructors. It contains the basic notions of abstract algebra through solved exercises as well as a 'True or False' section in each...

Features Filled with instructive examples and exercises to help build understanding Suitable for researchers, professionals and students, both in mathematics and computer scienceEvery chapter consists of exercises with solution provided online at www...

This research monograph develops the theory of relative nonhomogeneous Koszul duality. Koszul duality is a fundamental phenomenon in homological algebra and related areas of mathematics, such as algebraic topology, algebraic geometry, and representation...

This edited book is the result of many paper published by the authors through 15 years, and of new results on the theory of Generalized ODEs in abstract spaces. This book also covers applications to other types of differential equations. Many results of...

Since 1991, the group of ring theorists from China and Japan, joined by Korea from 1995 onwards, took turns to hold the quadrennial international conferences (sometimes also referred to as symposiums). As the proceedings of the eighth conference held in...

This book provides an introduction to fundamental methods and techniques of algebra over ordered fields. It is a revised and updated translation of the classic textbook Einfuhrung in die reelle Algebra. Beginning with the basics of ordered fields and...

This book reviews the theory of 'generalized B*-algebras' (GB*-algebras), a class of complete locally convex *-algebras which includes all C*-algebras and some of their extensions. A functional calculus and a spectral theory for GB*-algebras is...

This book examines ultrametric Banach algebras in general. It begins with algebras of continuous functions, and looks for maximal and prime ideals in connections with ultrafilters on the set of definition. The multiplicative spectrum has shown to be...

This book presents a compendium style account of a comprehensive mathematical journey from Arithmetic to Algebra. It contains material that is helpful to graduate and advanced undergraduate students in mathematics, university and college professors...

This monograph provides an exhaustive treatment of several classes of Noetherian rings and morphisms of Noetherian local rings. Chapters carefully examine some of the most important topics in the area, including  Nagata, F-finite and excellent rings,...

A thorough account of the methods that underlie the theory of subalgebras of finite von Neumann algebras, this book contains a substantial amount of current research material and is ideal for those studying operator algebras. The conditional expectation,...

This book contains a wealth of inequalities used in linear analysis, and explains in detail how they are used. The book begins with Cauchy's inequality and ends with Grothendieck's inequality, in between one finds the Loomis-Whitney inequality, maximal...

This is a short course on Banach space theory with special emphasis on certain aspects of the classical theory. In particular, the course focuses on three major topics: the elementary theory of Schauder bases, an introduction to Lp spaces, and an...

Clifford algebras have many well-known applications in physics, engineering, and computer graphics. Zeon algebras are subalgebras of Clifford algebras whose combinatorial properties lend them to graph-theoretic applications such as enumerating minimal...

Lattice theory extends into virtually every branch of mathematics, ranging from measure theory and convex geometry to probability theory and topology. A more recent development has been the rapid escalation of employing lattice theory for various...

Matrices and kernels with positivity structures, and the question of entrywise functions preserving them, have been studied throughout the 20th century, attracting recent interest in connection to high-dimensional covariance estimation. This is the first...

An indispensable companion to the book hailed an "expository masterpiece of the highest didactic value" by Zentralblatt MATH This solutions manual helps readers test and reinforce the understanding of the principles and real-world applications of...

This book is directed primarily at undergraduate and postgraduate students interested to get acquainted with the representation theory of Lie algebras. The book treats the case of the smallest simple Lie algebra, namely, the Lie algebra sl_2. It contains...

Functional analysis deals with infinite-dimensional spaces. Its results are among the greatest achievements of modern mathematics and it has wide-reaching applications to probability theory, statistics, economics, classical and quantum physics,...

Written by experts in their respective fields, this collection of pedagogic surveys provides detailed insight and background into five separate areas at the forefront of modern research in orthogonal polynomials and special functions at a level suited to...

This monograph provides an introduction and a survey of recent results in potential theory with respect to the Laplace-Beltrami operator D in several complex variables, with special emphasis on the unit ball in Cn. Topics covered include Poisson-Szegoe...

Hyperstructures represent a natural extension of classical algebraic structures. They were introduced in 1934 by the French mathematician Marty. Since then, hundreds of papers published on this subject. This book is devoted to the study of weak...

This volume collects chapters that examine representation theory as connected with affine Lie algebras and their quantum analogues, in celebration of the impact Vyjayanthi Chari has had on this area. The opening chapters are based on mini-courses given...

The theory of operator spaces is very recent and can be described as a non-commutative Banach space theory. An 'operator space' is simply a Banach space with an embedding into the space B(H) of all bounded operators on a Hilbert space H. The first part...

In this book, three authors introduce readers to strong approximation methods, analytic pro-p groups and zeta functions of groups. Each chapter illustrates connections between infinite group theory, number theory and Lie theory. The first introduces the...

This second edition covers essentially the same topics as the first. However, the presentation of the material has been extensively revised and improved. In addition, there are two new chapters, one dealing with the fundamental theorem of finitely...

Professor Retherford's aim in this book is to provide the reader with a virtually self-contained treatment of Hilbert space theory, leading to an elementary proof of the Lidskij trace theorem. He assumes the reader is familiar with only linear algebra...

The Langlands Programme is one of the most important areas in modern pure mathematics. The importance of this volume lies in its potential to recast many aspects of the programme in an entirely new context. For example, the morphisms in the monomial...

This concise monograph explores how core ideas in Hardy space function theory and operator theory continue to be useful and informative in new settings, leading to new insights for noncommutative multivariable operator theory. Beginning with a review of...

This book focuses on the major applications of martingales to the geometry of Banach spaces, and a substantial discussion of harmonic analysis in Banach space valued Hardy spaces is also presented. It covers exciting links between super-reflexivity and...