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
algebra.
This PDF covers the
following topics related to Abstract Algebra : The Integers, Groups, Cyclic
Groups, Permutation Groups, Cosets and Lagrange’s Theorem, Matrix Groups and
Symmetry, Isomorphisms, Homomorphisms, The Structure of Groups, Group Actions,
Vector Spaces.
This book covers the following topics: Group, Normal
subgroups and Quotient groups, homomorphism, isomorphism, Cayleys theorem,
permutation groups, Sylow’s Theorems, Rings,Polynomial rings, Vector spaces,
Extension field.
This note covers the
following topics: Integers, monomials, and monoids, Direct Products and
Isomorphism, Groups, Subgroups, Groups of permutations, Number theory, Rings,
Ideals, Rings and polynomial factorization, Grobner bases.
This note
explains the following topics: Sets and Functions, Factorization and the
Fundamental Theorem of Arithmetic, Groups, Permutation Groups and Group Actions,
Rings and Fields, Field Extensions and Galois Theory, Galois Theory.
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 note covers the following
topics: Group Theory, classification of cyclic subgroups, cyclic groups,
Structure of Groups, orbit stabilizer theorem and conjugacy, Rings and Fields,
homomorphism and isomorphism, ring homomorphism, polynomials in an indeterminant.
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
book explains the following topics: Group Theory, Subgroups, Cyclic
Groups, Cosets and Lagrange's Theorem, Simple Groups, Solvable Groups, Rings and
Polynomials, Galois Theory, The Galois Group of a Field Extension, Quartic
Polynomials.
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 covers the following topics related to Abstract Algebra:
The Integers, Foundations, Groups, Group homomorphisms and isomorphisms, Algebraic structures, Error correcting codes,
Roots of polynomials, Moduli for polynomials and Nonsolvability by radicals.
Covered
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
These notes give a concise exposition of the
theory of fields, including the Galois theory of finite and infinite extensions
and the theory of transcendental extensions.
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.
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
transform.
The book, Algebra: Abstract and Concrete provides a thorough introduction to
algebra at a level suitable for upper level
undergraduates and beginning graduate students. The book addresses the
conventional topics: groups, rings, fields, and linear algebra, with symmetry as
a unifying theme.