This note covers the following topics:
Set theory, Group theory, Ring theory, Isomorphism theorems, Burnsides formula,
Field theory and Galois theory, Module theory, Commutative algebra, Linear
algebra via module theory, Homological algebra, Representation theory.
This book aims
to give an introduction to using GAP with material appropriate for an
undergraduate abstract algebra course. It does not even attempt to give an
introduction to abstract algebra, there are many excellent books which do this.
Topics covered includes: The GGAP user interface, Rings, Groups, Linear Algebra,
Fields and Galois Theory, Number Theory.
This text is
intended for a one- or two-semester undergraduate course in abstract algebra.
Topics covered includes: The Integers, Groups, Cyclic Groups, Permutation
Groups, Cosets and Lagrange’s Theorem, Algebraic Coding Theory, Isomorphisms,
Normal Subgroups and Factor Groups, Matrix Groups and Symmetry, The Sylow
Theorems , Rings, Polynomials, Integral Domains, Vector Spaces, Finite Fields.
This note covers the
following topics: Groups, Bijections, Commutativity, Frequent groups and groups
with names, Subgroups, Group generators, Plane groups, Orders of groups and
elements, One-generated subgroups, Permutation groups, Group homomorphisms,
Group isomorphisms, RSA public key encryption scheme, Centralizer and the class
equation, Normal subgroups, The isomorphism theorems, Fundamental Theorem of
Finite Abelian Groups, Quotient rings, Prime ideals and maximal ideals, Unique
factorization domains, Modules, Fields, Splitting fields, Derivatives in
This book covers
the following topics: Algebraic Reorientation, Matrices, Groups, First Theorems,
Orders and Lagrange’s Theorem, Subgroups, Cyclic Groups and Cyclic Subgroups,
Isomorphisms, Cosets, Quotient Groups, Symmetric Groups, Rings and Fields.
This book is
a gentle introduction to abstract algebra. It is ideal as a text for a one
semester course designed to provide a rst exposure of the subject to students in
mathematics, science, or engineering. Covered topics are: Divisibility in the
Integers, Rings and Fields, Vector Spaces, Spaces, Groups, Sets, Functions, and
This note explains the following
topics: Linear Transformations, Algebra Of Linear Transformations,
Characteristic Roots, Characteristic Vectors, Matrix Of Transformation,
Canonical Form, Nilpotent Transformation, Simple Modules, Simi-simple Modules,
Free Modules, Noetherian And Artinian Modules, Noetherian And Artinian Rings,
Smith Normal Form, Finitely Generated Abelian Groups.
topics: Preliminaries, Integers, Groups, Cyclic Groups, Permutation Groups,
Cosets and Lagrange's Theorem, Introduction to Cryptography, Algebraic Coding
Theory, Isomorphisms, Homomorphisms, Matrix Groups and Symmetry, The Structure of Groups, Group
Actions, The Sylow Theorems, Rings, Polynomials, Integral Domains, Lattices and
Boolean Algebras, Vector Spaces, Fields and Galois Theory
Author(s): Thomas W. Judson, Stephen F. Austin State University
This is a foundational textbook on abstract algebra with emphasis on
linear algebra. Covered topics are: Background and Fundamentals of Mathematics,
Groups, Rings, Matrices and Matrix Rings and Linear Algebra.
book covers the following topics: Binary Operations, Introduction to Groups, The Symmetric Groups, Subgroups, The
Group of Units of Zn, Direct Products of Groups, Isomorphism of Groups, Cosets
and Lagrange s Theorem, Introduction to Ring Theory, Axiomatic Treatment of R N
Z Q and C, The Quaternions, The Circle Group.
Edwin Clark, Department of Mathematics, University of South Florida
This note covers the following topics: Basic Algebra of Polynomials,
Induction and the Well ordering Principle, Sets, Some counting principles, The
Integers, Unique factorization into primes, Prime Numbers, Sun Ze's Theorem,
Good algorithm for exponentiation, Fermat's Little Theorem, Euler's Theorem,
Primitive Roots, Exponents, Roots, Vectors and matrices, Motions in two and
three dimensions, Permutations and Symmetric Groups, Groups: Lagrange's Theorem,
Euler's Theorem, Rings and Fields, Cyclotomic polynomials, Primitive roots,
Group Homomorphisms, Cyclic Groups, Carmichael numbers and witnesses, More on
groups, Finite fields, Linear Congruences, Systems of Linear Congruences,
Abstract Sun Ze Theorem and Hamiltonian Quaternions.
This note covers the following topics: Natural Numbers, Principles of
Counting, Integers and Abelian groups, Divisibility, Congruences, Linear
Diophantine equations, Subgroups of Abelian groups, Commutative Rings, A little
Boolean Algebra, Fields, Polynomials over a Field, Quotients of Abelian groups,
Orders of Abelian groups, Linear Algebra over, Nonabelian groups, Groups of
Symmetries of Platonic Solids, Counting Problems involving Symmetry, Proofs of
theorems about group actions, Homomorphisms between groups, The Braid Group, The
Chinese remainder theorem, Quotients of polynomial rings, The finite Fourier
This study guide is intended to help students who are beginning to
learn about abstract algebra. This book covers the following topics: Integers,
Functions, Groups, Polynomials, Commutative Rings, Fields.
This study guide now contains over 600 problems, and more than half
have detailed solutions, while about a fifth have either an answer or a hint. The ideal way to
use the study guide is to work on a solved problem, and if you get stuck, just
peek at the solution long enough to get started again.
This is a text for the basic graduate sequence in abstract algebra,
offered by most universities. This book explains the fundamental algebraic
structures, namely groups, rings, fields and modules, and maps between these