This book explains the following topics, Group Theory, Subgroups, Cyclic Groups, Cosets and Lagranges Theorem, Simple Groups, Solvable Groups, Rings and Polynomials, Galois Theory, The Galois Group of a Field Extension, Quartic Polynomials.
This note explains basic concepts like sets and relations and progressing
to advanced topics such as group theory, rings, and fields also it covers
fundamental theorems like Lagranges theorem and explores key concepts like
permutations and quotient groups.
This PDF covers the
following topics related to Abstract Algebra, The Integers, Groups, Cyclic
Groups, Permutation Groups, Cosets and Lagranges Theorem, Matrix Groups and
Symmetry, Isomorphisms, Homomorphisms, The Structure of Groups, Group Actions,
Vector Spaces.
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 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 book explains the following topics, Group Theory, Subgroups, Cyclic Groups, Cosets and Lagranges Theorem, Simple Groups, Solvable Groups, Rings and Polynomials, Galois Theory, The Galois Group of a Field Extension, Quartic Polynomials.
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
Relations.
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.