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Abstract Algebra


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Designs and Their Codes
Designs and Their Codes
by E. F. Assmus
Publisher Comments
Algebraic coding theory has in recent years been increasingly applied to the study of combinatorial designs. This book gives an account of many of those applications together with a thorough general introduction to both design theory and coding theory... (read more)

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Lecture Notes in Mathematics #1988: Introduction to Complex Reflection Groups and Their Braid Groups
Lecture Notes in Mathematics #1988: Introduction to Complex Reflection Groups and Their Braid Groups
by Brou
Publisher Comments
Weyl groups are particular cases of complex reflection groups, i.e. finite subgroups of GLr(C) generated by (pseudo)reflections. These are groups whose polynomial ring of invariants is a polynomial algebra. It has recently been discovered that complex... (read more)

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London Mathematical Society Lecture Notes #373: Smoothness, Regularity and Complete Intersection
London Mathematical Society Lecture Notes #373: Smoothness, Regularity and Complete Intersection
by Javier Majadas
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Written to complement standard texts on commutative algebra, this short book gives complete and relatively easy proofs of important results, including the standard results involving localisation of formal smoothness (M. Andr ) and localisation of... (read more)

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Cambridge Tracts in Mathematics #188: Modern Approaches to the Invariant-Subspace Problem
Cambridge Tracts in Mathematics #188: Modern Approaches to the Invariant-Subspace Problem
by Isabelle Chalendar
Publisher Comments
One of the major unsolved problems in operator theory is the fifty-year-old invariant subspace problem, which asks whether every bounded linear operator on a Hilbert space has a nontrivial closed invariant subspace. This book presents some of the major... (read more)

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Semirings and Affine Equations Over Them: Theory and Applications
Semirings and Affine Equations Over Them: Theory and Applications
by Jonathan S. Golan
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Semiring theory stands with a foot in each of two mathematical domains. The first being abstract algebra and the other the fields of applied mathematics such as optimization theory, the theory of discrete-event dynamical systems, automata theory, and... (read more)

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Modern Algebra With Applications 2ND Edition
Modern Algebra With Applications 2ND Edition
by William J Gilbert
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Praise for the first edition "This book is clearly written and presents a large number of examples illustrating the theory . . . there is no other book of comparable content available. Because of its detailed coverage of applications generally neglected... (read more)

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Introduction To Lie Algebras and Representation Theory
Introduction To Lie Algebras and Representation Theory
by James E. Humphreys
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This book is designed to introduce the reader to the theory of semisimple Lie algebras over an algebraically closed field of characteristic 0, with emphasis on representations. A good knowledge of linear algebra (including eigenvalues, bilinear forms... (read more)

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Foundations of Micropolar Mechanics (Springerbriefs in Applied Sciences and Technology / Springer)
Foundations of Micropolar Mechanics (Springerbriefs in Applied Sciences and Technology / Springer)
by Victor A Eremeyev
Publisher Comments
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... (read more)

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Cambridge Studies in Advanced Mathematics #72: Galois Theories
Cambridge Studies in Advanced Mathematics #72: Galois Theories
by Francis Borceux
Publisher Comments
Starting from the classical finite-dimensional Galois theory of fields, this book develops Galois theory in a much more general context. The authors first formalize the categorical context in which a general Galois theorem holds, and then give... (read more)

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Lattice-ordered Rings and Modules (10 Edition)
Lattice-ordered Rings and Modules (10 Edition)
by Stuart A. Steinberg
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This book provides an exposition of the algebraic aspects of the theory of lattice-ordered rings and lattice-ordered modules. All of the background material on rings, modules, and lattice-ordered groups necessary to make the work self-contained and... (read more)

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Families of Exponentials: The Method of Moments in Controllability Problems for Distributed Parameter Systems
Families of Exponentials: The Method of Moments in Controllability Problems for Distributed Parameter Systems
by Sergei A. Avdonin
Publisher Comments
In this book, the authors present the newly developed theory of non-harmonic Fourier series and its applications to the control of distributed parameter systems, and they extend the theory to include vector exponential series. The first part of the book... (read more)

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Lecture Notes in Physics #858: An Introduction to Non-Abelian Discrete Symmetries for Particle Physicists
Lecture Notes in Physics #858: An Introduction to Non-Abelian Discrete Symmetries for Particle Physicists
by Hajime Ishimori
Publisher Comments
These lecture notes provide a tutorial review of non-Abelian discrete groups and show some applications to issues in physics where discrete symmetries constitute an important principle for model building in particle physics.... (read more)

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A Book of Abstract Algebra
A Book of Abstract Algebra
by Charles Pinter
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Accessible but rigorous, this outstanding text encompasses all of the topics covered by a typical course in elementary abstract algebra. Its easy-to-read treatment offers an intuitive approach, featuring informal discussions followed by thematically... (read more)

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Science Networks. Historical Studies #45: Proofs of the Cantor-Bernstein Theorem: A Mathematical Excursion
Science Networks. Historical Studies #45: Proofs of the Cantor-Bernstein Theorem: A Mathematical Excursion
by Arie Hinkis
Publisher Comments
This book offers an excursion through the developmental area of research mathematics. It presents some 40 papers, published between the 1870s and the 1970s, on proofs of the Cantor-Bernstein theorem and the related Bernstein division theorem. While the... (read more)

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Symmetry, Representations, and Invariants
Symmetry, Representations, and Invariants
by Roe Goodman
Publisher Comments
Symmetry is a key ingredient in many mathematical, physical, and biological theories. Using representation theory and invariant theory to analyze the symmetries that arise from group actions, and with strong emphasis on the geometry and basic theory of... (read more)

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Abstract Algebra and Solution By Radicals (10 Edition)
Abstract Algebra and Solution By Radicals (10 Edition)
by John E. Maxfield
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This advanced undergraduate-level text was recommended for teacher education by The American Mathematical Monthly and praised as a "most readable book." An ideal introduction to groups and Galois theory, it provides students with an appreciation of... (read more)

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A Course in Galois Theory
A Course in Galois Theory
by D. J. H. Garling
Publisher Comments
From an elementary discussion of groups, fields and vector spaces, this introduction to Galois theory progresses to rings, extension fields, ruler-and-compass constructions, automorphisms and Galois correspondence.... (read more)

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Cime Summer Schools #60: Finite Geometric Structures and Their Applications: Lectures Given at a Summer School of the Centro Internazionale Matematico Estivo (C.I.M.E.) Held i
Cime Summer Schools #60: Finite Geometric Structures and Their Applications: Lectures Given at a Summer School of the Centro Internazionale Matematico Estivo (C.I.M.E.) Held i
by A Barlotti
Publisher Comments
R.C. Bose: Graphs and designs.- R.H. Bruck: Construction problems in finite projective spaces.- R.H.F. Denniston: Packings of PG(3,q).- J. Doyen: Recent results on Steiner triple systems.- H. Lüneburg: Gruppen und endliche projektive Ebenen.- J.A. Thas:... (read more)

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Geometrie Et Theorie Des Groupes
Geometrie Et Theorie Des Groupes
by Michel Coornaert
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The book is an introduction of Gromov's theory of hyperbolic spaces and hyperbolic groups. It contains complete proofs of some basic theorems which are due to Gromov, and emphasizes some important developments on isoperimetric inequalities, automatic... (read more)

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Galois Connections and Applications
Galois Connections and Applications
by K. Denecke
Publisher Comments
This book presents the main ideas of General Galois Theory as a generalization of Classical Galois Theory. It sketches the development of Galois connections through the last three centuries. Examples of Galois connections as powerful tools in Category... (read more)

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