Logo

Abstract Algebra

see also

Elementary Algebra (34)

e-books in Abstract Algebra category

Book cover: The Construction and Study of Certain Important AlgebrasThe Construction and Study of Certain Important Algebras
by - The Mathematical Society Of Japan ,
This is the reproduction of the beautiful lectures delivered by Professor C. Chevalley at the University of Tokyo in April-June 1954. Contents: Graded algebras; Tensor algebras; Clifford algebras; Some applications of exterior algebras.
(4196 views)
Book cover: The Algebra of InvariantsThe Algebra of Invariants
by - Cambridge, University Press ,
Invariant theory is a subject within abstract algebra that studies polynomial functions which do not change under transformations from a linear group. This book provides an English introduction to the symbolical method in the theory of Invariants.
(4872 views)
Book cover: An introduction to Noncommutative Projective GeometryAn introduction to Noncommutative Projective Geometry
by - arXiv ,
These lecture notes are an expanded version of the author's lectures at a graduate workshop. The main topics discussed are Artin-Schelter regular algebras, point modules, and the noncommutative projective scheme associated to a graded algebra.
(3946 views)

Book cover: An Introduction to the Algebra of QuanticsAn Introduction to the Algebra of Quantics
by - The Clarendon Press ,
The primary object of this book is that of explaining with all the clearness at my command the leading principles of invariant algebra, in the hope of making it evident to the junior student that the subject is attractive as well as important.
(4686 views)
Book cover: Set Theoretic Approach to Algebraic Structures in MathematicsSet Theoretic Approach to Algebraic Structures in Mathematics
by - Educational Publisher ,
This book brings out how sets in algebraic structures can be used to construct the most generalized algebraic structures, like set linear algebra / vector space, set ideals in groups and rings and semigroups, and topological set vector spaces.
(5046 views)
Book cover: Algebraic InvariantsAlgebraic Invariants
by - J. Wiley & Sons ,
This introduction to the classical theory of invariants of algebraic forms is divided into three parts: linear transformations; algebraic properties of invariants and covariants; symbolic notation of Aronhold and Clebsch.
(4595 views)
Book cover: An introduction to Algebra and TopologyAn introduction to Algebra and Topology
by - University of Luxemburg ,
These lecture notes are an elementary introduction to the language of categories and sheaves. From the table of contents: Linear algebra over a ring; The language of categories; Sheaves (Flabby sheaves and soft sheaves, Cohomology of sheaves).
(5341 views)
Book cover: Lectures On Unique Factorization DomainsLectures On Unique Factorization Domains
by - Tata Institute Of Fundamental Research ,
In this book we shall study some elementary properties of Krull rings and factorial rings, regular rings (local and factorial), and descent methods (Galoisian descent, the Purely inseparable case, formulae concerning derivations).
(4785 views)
Book cover: Noncommutative RingsNoncommutative Rings
by ,
From the table of contents: Morita equivalence (Hom, Bimodules, Projective modules ...); Localization and Goldie's theorem; Central simple algebras and the Brauer group; Maximal orders; Irreducible representations; Growth of algebras.
(5698 views)
Book cover: Lectures on Quadratic FormsLectures on Quadratic Forms
by - Tata Institute of Fundamental Research ,
From the table of contents: Vector groups and linear inequalities (Vector groups, Lattices, Characters, Diophantine approximations); Reduction of positive quadratic forms; Indefinite quadratic forms; Analytic theory of Indefinite quadratic forms.
(5592 views)
Book cover: Graduate AlgebraGraduate Algebra
by - Northwestern University ,
Contents: Groups; Group actions on sets; Normal series; Ring theory; Modules; Hom and tensor; Field theory; Galois theory; Applications of Galois theory; Infinite extensions; Categories; Multilinear algebra; More ring theory; Localization; etc.
(7544 views)
Book cover: Algebraic LogicAlgebraic Logic
by ,
Part I of the book studies algebras which are relevant to logic. Part II deals with the methodology of solving logic problems by (i) translating them to algebra, (ii) solving the algebraic problem, and (iii) translating the result back to logic.
(10003 views)
Book cover: Infinite-dimensional Lie AlgebrasInfinite-dimensional Lie Algebras
by - University of Edinburgh ,
Contents: Central extensions; Virasoro algebra; Heisenberg algebra; Enveloping algebras; Hands-on loop and affine algebras; Simple Lie algebras; Kac-Moody Lie algebras; Dynkin diagrams; Forms, Weyl groups and roots; Root spaces; Affine Lie algebras.
(6917 views)
Book cover: A Treatise on the Theory of InvariantsA Treatise on the Theory of Invariants
by - Project Gutenberg ,
The object of this book is to present in a volume of medium size the fundamental principles and processes and a few of the multitudinous applications of invariant theory, with emphasis upon both the nonsymbolical and the symbolical method.
(5925 views)
Book cover: Smarandache Near-ringsSmarandache Near-rings
by - American Research Press ,
Near-rings are one of the generalized structures of rings. This is a book on Smarandache near-rings where the Smarandache analogues of the near-ring concepts are developed. The reader is expected to have a background in algebra and in near-rings.
(7267 views)
Book cover: Smarandache RingsSmarandache Rings
by - American Research Press ,
The author embarked on writing this book on Smarandache rings (S-rings) specially to motivate both ring theorists and Smarandache algebraists to develop and study several important and innovative properties about S-rings.
(7310 views)
Book cover: Smarandache LoopsSmarandache Loops
by - American Research Press ,
The purpose of this book entirely lies in the study, introduction and examination of the Smarandache loops. We expect the reader to have a good background in algebra and more specifically a strong foundation in loops and number theory.
(5162 views)
Book cover: Smarandache Semirings, Semifields and Semivector SpacesSmarandache Semirings, Semifields and Semivector Spaces
by - American Research Press ,
This is the first book on the Smarandache algebraic structures that have two binary operations. Semirings are algebraic structures with two binary operations enjoying several properties and it is the most generalized structure.
(7401 views)
Book cover: Clifford Algebra, Geometric Algebra, and ApplicationsClifford Algebra, Geometric Algebra, and Applications
by - arXiv ,
These are lecture notes for a course on the theory of Clifford algebras. The various applications include vector space and projective geometry, orthogonal maps and spinors, normed division algebras, as well as simplicial complexes and graph theory.
(7674 views)
Book cover: Universal Algebra for Computer ScienceUniversal Algebra for Computer Science
by - Wagner Mathematics ,
A text on universal algebra with a strong emphasis on applications and examples from computer science. The text introduces signatures, algebras, homomorphisms, initial algebras, free algebras, and illustrates them with interactive applications.
(9585 views)
Book cover: New Directions in Hopf AlgebrasNew Directions in Hopf Algebras
by - Cambridge University Press ,
Hopf algebras have important connections to quantum theory, Lie algebras, knot and braid theory, operator algebras, and other areas. The book gives a clear picture of the current trends, with a focus on what will be important in future research.
(6647 views)
Book cover: An Introduction to Nonassociative AlgebrasAn Introduction to Nonassociative Algebras
by - Project Gutenberg ,
Concise study presents in a short space some of the important ideas and results in the theory of nonassociative algebras, with particular emphasis on alternative and (commutative) Jordan algebras. Written as an introduction for graduate students.
(8255 views)
Book cover: Commutator Theory for  Congruence Modular VarietiesCommutator Theory for Congruence Modular Varieties
by - Cambridge University Press ,
This book presents the basic theory of commutators in congruence modular varieties and some of its strongest applications. The authors take an algebraic approach, using some of the shortcuts that Taylor and others have discovered.
(6929 views)
Book cover: The OctonionsThe Octonions
by - University of California ,
The octonions are the largest of the four normed division algebras. The author describes them and their relation to Clifford algebras and spinors, Bott periodicity, projective and Lorentzian geometry, Jordan algebras, and the exceptional Lie groups.
(12422 views)
Book cover: Abstract Algebra: The Basic Graduate YearAbstract Algebra: The Basic Graduate Year
by ,
Text for a graduate course in abstract algebra, it covers fundamental algebraic structures (groups, rings, fields, modules), and maps between them. The text is written in conventional style, the book can be used as a classroom text or as a reference.
(12354 views)
Book cover: An Invitation to General Algebra and Universal ConstructionsAn Invitation to General Algebra and Universal Constructions
by - Henry Helson ,
From the contents: Free groups; Ordered sets, induction, and the Axiom of Choice; Lattices, closure operators, and Galois connections; Categories and functors; Universal constructions in category-theoretic terms; Varieties of algebras; etc.
(8196 views)
Book cover: Workbook in Higher AlgebraWorkbook in Higher Algebra
by ,
A set of notes for a Higher Algebra course. It covers Group Theory, Field and Galois Theory, Elementary Factorization Theory, Dedekind Domains, Module Theory, Ring Structure Theory, Tensor Products, Zorn’s Lemma and some Applications.
(10248 views)
Book cover: A Course in Universal AlgebraA Course in Universal Algebra
by - Springer-Verlag ,
Selected topics in universal algebra: an introduction to lattices, the most general notions of universal algebra, a careful development of Boolean algebras, discriminator varieties, the introduction to the basic concepts and results of model theory.
(15682 views)
Book cover: Lie AlgebrasLie Algebras
by ,
The Campbell Baker Hausdorff formula, sl(2) and its representations, classical simple algebras, Engel-Lie-Cartan-Weyl, conjugacy of Cartan subalgebras, simple finite dimensional algebras, cyclic highest weight modules, Serre’s theorem, and more.
(11717 views)