These are notes from a first term abstract algebra course, an introduction to groups, rings, and fields. There is an emphasis on specific examples.

I hope to get the notes for additional topics in abstract algebra written soon.

The first link in each item is to a Web page; the second is to a PDF (Adobe Acrobat) file. Use the PDF if you want to print it.

- Groups

[PDF] - Subgroups

[PDF] - Divisibility

[PDF] - Greatest common divisors; the
Euclidean and Extended Euclidean algorithms

[PDF] - Prime numbers

[PDF] - Modular
arithmetic

[PDF] - The group of units in the integers
mod n

[PDF] - Cyclic groups

[PDF] - Permutations

[PDF] - Direct products

[PDF] - The Structure
Theorem for Finitely Generated Abelian Groups

[PDF] (Examples only - the theorem is stated, but not proved) - Group homomorphisms and
isomorphisms

[PDF] - Cosets and Lagrange's theorem

[PDF] - Normal subgroups and quotient
groups

[PDF] - The First Isomorphism Theorem
and the Universal Property of the Quotient

[PDF] - Rings

[PDF] - Polynomial
rings; the Root and Factor Theorems; polynomial gcds

[PDF] - Ideals and subrings

[PDF] - Ring homomorphisms and
isomorphisms

[PDF] - Quotient rings

[PDF] - Quotient rings of polynomial rings

[PDF]

Send comments about this page to: Bruce.Ikenaga@millersville.edu.