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An introduction to Noncommutative Projective GeometryAn 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.
(407 views)

Hopf Algebras in General and in Combinatorial Physics: a practical introductionHopf 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.
(1168 views)

An Introduction to the Algebra of QuanticsAn 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.
(1299 views)

Set Theoretic Approach to Algebraic Structures in MathematicsSet 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.
(1624 views)

Algebraic InvariantsAlgebraic 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.
(1153 views)

An introduction to Algebra and TopologyAn 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).
(1974 views)

Lectures On Unique Factorization DomainsLectures 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).
(2304 views)

Noncommutative RingsNoncommutative 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.
(2973 views)

Lectures on Quadratic FormsLectures 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.
(3087 views)

Graduate AlgebraGraduate 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.
(4066 views)

Algebraic LogicAlgebraic 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.
(6157 views)

Infinite-dimensional Lie AlgebrasInfinite-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.
(3390 views)

A Treatise on the Theory of InvariantsA 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.
(3643 views)

Introduction to Non-Linear AlgebraIntroduction to Non-Linear Algebra
by V. Dolotin, A. Morozov - arXiv , 2008
Concise introduction to a relatively new subject of non-linear algebra. This powerful science is based on the notions of discriminant and resultant, which today can be effectively studied both analytically and by modern computer facilities.
(5030 views)

Smarandache Near-ringsSmarandache 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.
(2875 views)

Smarandache RingsSmarandache 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.
(2895 views)

Smarandache LoopsSmarandache 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.
(2871 views)

Smarandache Semirings, Semifields and Semivector SpacesSmarandache 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.
(2831 views)

Clifford Algebra, Geometric Algebra, and ApplicationsClifford 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.
(6551 views)

Universal Algebra for Computer ScienceUniversal 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.
(6422 views)

New Directions in Hopf AlgebrasNew 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.
(4387 views)

An Introduction to Nonassociative AlgebrasAn 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.
(5237 views)

Commutator Theory for  Congruence Modular VarietiesCommutator 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.
(4726 views)

The OctonionsThe 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.
(9048 views)

Abstract Algebra: The Basic Graduate YearAbstract 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.
(8723 views)

An Invitation to General Algebra and Universal ConstructionsAn 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.
(5543 views)

Workbook in Higher AlgebraWorkbook 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.
(7053 views)

A Course in Universal AlgebraA 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.
(12253 views)

Lie AlgebrasLie 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.
(5898 views)