subcategories
Commutative Algebra (19)
Fields & Galois Theory (12)
Group Theory (39)
Introductory (18)
Order, Lattices, Representation Theory (13)
see also
Elementary Algebra (39)
e-books in Abstract Algebra category
Hopf Algebras, Quantum Groups and Yang-Baxter Equationsby Florin Felix Nichita (ed.) - MDPI AG , 2019
Various aspects of the Yang-Baxter equation, related algebraic structures, and applications are presented. The algebraic approach to bundles in non-commutative geometry and the definition of quantum real weighted projective spaces are reviewed.
(6892 views)
On Lie Algebras Of Prime Characteristicby George B. Seligman - American Mathematical Society , 1956
The purpose of the present memoir is to demonstrate the applicability, under certain restrictions on the algebra and the base field, of the techniques used in the determination of all simple Lie algebras of characteristic zero.
(7079 views)
The Construction and Study of Certain Important Algebrasby Claude Chevalley - The Mathematical Society Of Japan , 1955
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.
(10962 views)
The Algebra of Invariantsby J.H. Grace, A. Young - Cambridge, University Press , 1903
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.
(12544 views)
An introduction to Noncommutative Projective Geometryby D. Rogalski - arXiv , 2014
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.
(10497 views)
Hopf Algebras in General and in Combinatorial Physics: a practical introductionby G.H.E. Duchamp, et al. - arXiv , 2008
This tutorial is intended to give an accessible introduction to Hopf algebras. The mathematical context is that of representation theory, and we also illustrate the structures with examples taken from combinatorics and quantum physics.
(10371 views)
An Introduction to the Algebra of Quanticsby E.B. Elliott - The Clarendon Press , 1913
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.
(11402 views)
Set Theoretic Approach to Algebraic Structures in Mathematicsby W. B. Vasantha Kandasamy, Florentin Smarandache - Educational Publisher , 2013
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.
(12186 views)
Algebraic Invariantsby Leonard E. Dickson - J. Wiley & Sons , 1914
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.
(11600 views)
An introduction to Algebra and Topologyby Pierre Schapira - University of Luxemburg , 2012
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).
(11759 views)
Lectures On Unique Factorization Domainsby P. Samuel - Tata Institute Of Fundamental Research , 1964
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).
(11247 views)
Noncommutative Ringsby Michael Artin , 1999
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.
(12046 views)
Lectures on Quadratic Formsby C.L. Siegel - Tata Institute of Fundamental Research , 1957
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.
(12198 views)
Graduate Algebraby Leonard Evens - Northwestern University , 1999
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.
(15205 views)
Algebraic Logicby H. Andreka, I. Nemeti, I. Sain , 2003
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.
(17939 views)
Infinite-dimensional Lie Algebrasby Iain Gordon - University of Edinburgh , 2009
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.
(13388 views)
A Treatise on the Theory of Invariantsby Oliver E. Glenn - Project Gutenberg , 2006
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.
(12158 views)
Smarandache Near-ringsby W. B. Vasantha Kandasamy - American Research Press , 2002
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.
(14056 views)
Smarandache Ringsby W. B. Vasantha Kandasamy - American Research Press , 2002
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.
(13410 views)
Smarandache Loopsby W. B. Vasantha Kandasamy - American Research Press , 2002
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.
(11532 views)
Smarandache Semirings, Semifields and Semivector Spacesby W. B. Vasantha Kandasamy - American Research Press , 2002
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.
(13563 views)
Clifford Algebra, Geometric Algebra, and Applicationsby Douglas Lundholm, Lars Svensson - arXiv , 2009
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.
(15739 views)
Universal Algebra for Computer Scienceby Eric G. Wagner - Wagner Mathematics , 2006
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.
(16678 views)
An Introduction to Nonassociative Algebrasby Richard D. Schafer - Project Gutenberg , 2008
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.
(15219 views)
Commutator Theory for Congruence Modular Varietiesby Ralph Freese, Ralph McKenzie - Cambridge University Press , 1987
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.
(13501 views)
The Octonionsby John C. Baez - University of California , 2001
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.
(20246 views)
Abstract Algebra: The Basic Graduate Yearby Robert B. Ash , 2002
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.
(19868 views)
An Invitation to General Algebra and Universal Constructionsby George M. Bergman - Henry Helson , 1998
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.
(15194 views)
Workbook in Higher Algebraby David Surowski , 1992
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.
(17747 views)
A Course in Universal Algebraby S. Burris, H.P. Sankappanavar - Springer-Verlag , 1982
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.
(22767 views)
Lie Algebrasby Shlomo Sternberg , 2004
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.
(18843 views)