Abstract Algebra Home

All my notes are based on the Math 113 course at UC Berkeley. The midterm and practice questions are also taken from the course.

Topics:

In no particular order. Extensive guides on:
Introductory Ring Theory
Half-Factorial Domains
Vector Spaces in Abstract Algebra
Abstract algebra for ML
Extension Fields
Factorizations in Integral domains
Fields
Group Actions
Cryptography
Group Isomorphisms and Homomorphisms

Proofs:

Taken from problems I found interesting or fundamental theorems.
Homomorphism is Injective if and only if the kernel is trivial
All Ideals in integers mod n
Cayley's Theorem (Important applications)
Order of elements in Cyclic Groups
Proof of Kronecker's Theorem
Prove there are no injective homomorphisms
Why every prime element is irreducible in an integral domain.

Quick Guides:

All Ideals in integers mod n
Normal function of euclidian integers
Behaviors of Z modulo
Organization of R polynomial x by classification of R

Review:

Completed solutions of given practice problems and midterms.
Group Theory and Basics:
Midterm 1
Practice Midterm 1
Ring and Field Theory:
Practice Final