## subcategories

**Commutative Algebra** (20)

**Fields & Galois Theory** (13)

**Group Theory** (42)

**Introductory** (18)

**Order, Lattices, Representation Theory** (15)

## see also

**Elementary Algebra** (37)

## e-books in Abstract Algebra category

**Hopf Algebras, Quantum Groups and Yang-Baxter Equations**

by

**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.

(

**3367**views)

**On Lie Algebras Of Prime Characteristic**

by

**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.

(

**4160**views)

**The Construction and Study of Certain Important Algebras**

by

**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.

(

**8218**views)

**The Algebra of Invariants**

by

**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.

(

**8954**views)

**An introduction to Noncommutative Projective Geometry**

by

**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.

(

**7463**views)

**Hopf Algebras in General and in Combinatorial Physics: a practical introduction**

by

**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.

(

**7919**views)

**An Introduction to the Algebra of Quantics**

by

**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.

(

**8377**views)

**Set Theoretic Approach to Algebraic Structures in Mathematics**

by

**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.

(

**8965**views)

**Algebraic Invariants**

by

**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.

(

**8323**views)

**An introduction to Algebra and Topology**

by

**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).

(

**9177**views)

**Lectures On Unique Factorization Domains**

by

**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).

(

**8222**views)

**Noncommutative Rings**

by

**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.

(

**9020**views)

**Lectures on Quadratic Forms**

by

**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.

(

**9390**views)

**Graduate Algebra**

by

**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.

(

**11793**views)

**Algebraic Logic**

by

**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.

(

**14398**views)

**Infinite-dimensional Lie Algebras**

by

**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.

(

**10748**views)

**A Treatise on the Theory of Invariants**

by

**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.

(

**9524**views)

**Smarandache Near-rings**

by

**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.

(

**11072**views)

**Smarandache Rings**

by

**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.

(

**10814**views)

**Smarandache Loops**

by

**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.

(

**8709**views)

**Smarandache Semirings, Semifields and Semivector Spaces**

by

**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.

(

**10803**views)

**Clifford Algebra, Geometric Algebra, and Applications**

by

**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.

(

**12202**views)

**Universal Algebra for Computer Science**

by

**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.

(

**13845**views)

**New Directions in Hopf Algebras**

by

**S. Montgomery, H. Schneider**-

**Cambridge University Press**,

**2002**

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.

(

**10152**views)

**An Introduction to Nonassociative Algebras**

by

**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.

(

**11887**views)

**Commutator Theory for Congruence Modular Varieties**

by

**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.

(

**10599**views)

**The Octonions**

by

**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.

(

**17112**views)

**Abstract Algebra: The Basic Graduate Year**

by

**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.

(

**16806**views)

**An Invitation to General Algebra and Universal Constructions**

by

**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.

(

**12129**views)

**Workbook in Higher Algebra**

by

**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.

(

**14524**views)

**A Course in Universal Algebra**

by

**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.

(

**19611**views)

**Lie Algebras**

by

**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.

(

**15731**views)