Algebra Books

When we began to consider the scope of this book, we envisaged a catalogue supplying at least one abstract definition for any finitely­ generated group that the reader might propose. But we soon realized that more or less arbitrary restrictions are...

Dieses Lehrbuch ermöglicht dem Leser einen leichten Einstieg in die Matrixrechnung. Matrizen und Vektoren bilden eine wesentliche Grundlage vieler quantitativer Modelle und Methoden sowohl in der ökonomischen Forschung als auch in der industriellen...

Leonid Ryvkin gives a motivated and self-sustainedintroduction to n-plectic geometry with a special focus on symmetries. Therelevant algebraic structures from scratch are developed. The author generalizesknown symplectic notions, notably observables and...

Konrad Schöbel aims to lay the foundations for a consequent algebraic geometric treatment of variable Separation, which is one of the oldest and most powerful methods to construct exact solutions for the fundamental equations in classical and quantum...

Sara Confalonieri presents an overview of Cardano's mathematical treatises and, in particular, discusses the writings that deal with cubic equations. The author gives an insight into the latest of Cardano's algebraic works, the De Regula Aliza (1570),...

This volume contains the articles contributed to the Conference on Categorical Algebra, held June 7-12,1965, at the San Diego campus of the University of California under the sponsorship of the United States Air Force Office of...

The study of the structure of Lie algebras over arbitrary fields is now a little more than thirty years old. The first papers, to my know­ ledge, which undertook this study as an end in itself were those of JACOBSON (" Rational...

In this volume we present a survey of the theory of Galois module structure for rings of algebraic integers. This theory has experienced a rapid growth in the last ten to twelve years, acquiring mathematical depth and ...

Und dann erst kommt der "Ab -ge - sa. ng\' da. /3 der nidlt kurz und nicht zu la. ng, From "Die Meistersinger von Nürnberg", Richard Wagner This final volume is concerned with some of the developments of the subject in the...

17):~t? L It CIFDr- ! wei! unsre Weisheit Einfalt ist, From "Lohengrin", Richard Wagner At the time of the appearance of the first volume of this work in 1967, the tempestuous development of finite group theory had already made...

Three years have passed since the publication of the Russian edition of this book, during which time the method described has found new applications. In [26], the author has introduced the concept of the periodic product of two...

The translator of a mathematical work faces a task that is at once fascinating and frustrating. He has the opportunity of reading closely the work of a master mathematician. He has the duty of retaining as far as possible the...

The theory of rings of quotients has its origin in the work of (j). Ore and K. Asano on the construction of the total ring of fractions, in the 1930's and 40's. But the subject did not really develop until the end of the...

The fundamental problem of the theory of Fourier series consists of the investigation of the connections between the metric properties of the function expanded, the behavior of its Fourier coefficients {cn} with respect to an...

The axioms of a complex Banach algebra were very happily chosen. They are simple enough to allow wide ranging fields of application, notably in harmonic analysis, operator theory and function algebras. At the same time they are...

By definition, an indefinite inner product space is a real or complex vector space together with a symmetric (in the complex case: hermi­ tian) bilinear form prescribed on it so that the corresponding quadratic form assumes...

Als ich im Jahre 1958 mit den Vorarbeiten zu diesem Buch begann, schien es noch moglich, eine einigermal3en vollstandige Darstellung der Strukturtheorie endlicher Gruppen in einem Bande zu geben. Die stiir­ mische Entwicklung,...

The words "microdifferential systems in the complex domain" refer to seve­ ral branches of mathematics: micro local analysis, linear partial differential equations, algebra, and complex analysis. The microlocal point of view...

Content and Subject Matter: This research monograph deals with two main subjects, namely the notion of equimultiplicity and the algebraic study of various graded rings in relation to blowing ups. Both subjects are clearly...

The invention of quantum groups is one of the outstanding achievements of mathematical physics and mathematics in the late twentieth century. The birth of the new theory and its rapid development are results of a strong...

The method of normal forms is usually attributed to Poincaré although some of the basic ideas of the method can be found in earlier works of Jacobi, Briot and Bouquet. In this book, A.D.Bruno gives an account of the work of...

Algebraic logic is a subject in the interface between logic, algebra and geometry, it has strong connections with category theory and combinatorics. Tarski's quest for finding structure in logic leads to cylindric-like algebras as studied in this book,...

This book features survey and research papers from The Abel Symposium 2011: Algebras, quivers and representations, held in Balestrand, Norway 2011. It examines a very active research area that has had a growing influence and profound impact in many other...

Method of Coefficients: an algebraic characterization and recent applications.- Partitions With Distinct Evens.- A factorization theorem for classical group characters, with applications to plane partitions and rhombus tilings.- On multivariate...

During the springs of 2011 and 2012, the author was invited by Peking University to give an advanced undergraduate algebra course (once a week over two months each year). This book was written during and for that course. By no...

Classical valuation theory has applications in number theory and class field theory as well as in algebraic geometry, e.g. in a divisor theory for curves. But the noncommutative equivalent is mainly applied to finite dimensional skewfields. Recently...

This book presents advances in matrix and tensor data processing in the domain of signal, image and information processing. The theoretical mathematical approaches are discusses in the context of potential applications in sensor and cognitive systems...

The book offers a new approach to information theory that is more general then the classical approach by Shannon. The classical definition of information is given for an alphabet of symbols or for a set of mutually exclusive propositions (a partition of...

The book presents foundations of the micropolar continuum mechanics including a short but comprehensive introduction of stress and strain measures, derivation of motion equations and discussion of the difference between Cosserat and classical (Cauchy)...

This textbook introduces students of economics to the fundamental notions and instruments in linear algebra. Linearity is used as a first approximation to many problems that are studied in different branches of science, including economics and other...

The Abel Symposium 2009 "Combinatorial aspects of Commutative Algebra and Algebraic Geometry", held at Voss, Norway, featured talks by leading researchers in the field. This is the proceedings of the Symposium, presenting contributions on syzygies,...

Assuming only basic algebra and Galois theory, the book develops the method of "algebraic patching" to realize finite groups and, more generally, to solve finite split embedding problems over fields. The method succeeds over rational function fields of...

This book covers the modular invariant theory of finite groups, the case when the characteristic of the field divides the order of the group, a theory that is more complicated than the study of the classical non-modular case. Largely self-contained, the...

In this book, regular structures are de ned as periodic structures consisting of repeated elements (translational symmetry) as well as structures with a geom- ric symmetry. Regular structures have for a long time been attracting the attention of...

Steps forward in mathematics often reverberate in other scientific disciplines, and give rise to innovative conceptual developments or find surprising technological applications. This volume brings to the forefront some of the proponents of the...

Part I An ABC on Compositionality.- Part II Manifestations of Linearity.- Part III More Example Applications.- Part IV Informatic Geometry.- Part V. Spatio-Temporal Geometry.- Part VI Geometry and Topology in Computation.

This volume exposes the theory of biset functors for finite groups, which yields a unified framework for operations of induction, restriction, inflation, deflation and transport by isomorphism. The first part recalls the basics on biset categories and...

Over last decades low-dimensional materials are in focus of physics and chemistry as well as of material and other natural sciences. Like Vitaly Ginzburg has foreseen 30 years ago, low dimensionality offers physical phenomena...

R. Baer: Complementation in finite gropus.- M. Lazard: Groupes, anneaux de Lie et problème de Burnside.- J. Tits: Sur les groupes algébriques afffines. Théorèmes fondamentaux de structure. Classification des groupes semisimples et géométries associées.

Mathematics Basics.- Elements of Lattice Theory.- Basics of Information Retrieval Technology.- Lattice-Based Retrieval Systems.- Boolean Retrieval.- Lattices of Subspaces and Projectors.- Vector Space Retrieval.- Fuzzy Algebra-Based Retrieval.-...

Preliminaries.- The Jordan normal form of the Coxeter transformation.- Eigenvalues, splitting formulas and diagrams Tp,q,r.- R. Steinberg's theorem, B. Kostant's construction.- The affine Coxeter transformation.

Basic Hodge Theory.- Compact Kähler Manifolds.- Pure Hodge Structures.- Abstract Aspects of Mixed Hodge Structures.- Mixed Hodge Structures on Cohomology Groups.- Smooth Varieties.- Singular Varieties.- Singular Varieties: Complementary Results.-...

Generalities on algebraic varieties.- Generalities on algebraic groups.- Grassmannian.- Determinantal varieties.- Symplectic Grassmannian.- Orthogonal Grassmannian.- The standard monomial theoretic basis.- Review of GIT.- Invariant theory.- SLn(K)-action...

The Concept of Symmetry.- Science Is Founded on Symmetry.- Symmetry in Physics.- The Symmetry Principle.- Application of Symmetry.- Approximate Symmetry, Spontaneous Symmetry Breaking.- Cosmic Considerations.- The Mathematics of Symmetry: Group Theory.-...

This book covers the development of reciprocity laws, starting from conjectures of Euler and discussing the contributions of Legendre, Gauss, Dirichlet, Jacobi, and Eisenstein. Readers knowledgeable in basic algebraic number...