Abstract Algebra II

There is no required textbook. All lecture notes will be posted here. For further reading I recommend Michael Artin's Algebra, Charles C. Pinter's Book of Abstract Algebra and John Stillwell's Elements of Algebra.

Office Hours: TBA

Here is the syllabus.
Course Notes    (and here are the old notes from Algebra I)
Item Date Information
Homework 1
Solutions in the Notes
Fri Feb 1 The Classical Problem of Algebra
Definition of Fields and Subfields
The Lattice of Subfields
The Galois Group
The Fundamental Theorem of Galois Theory
Homework 2
Solutions in the Notes
Fri Feb 15 Rings and Subrings
Ring Homomorphisms
Ideals and Quotient Rings
Correspondence and Isomorphism Theorems
Descartes' Factor Theorem
Z and F[x] are PIDs
Exam 1
Solutions
Wed Feb 20
Homework 3
Solutions in the Notes
Fri Mar 8 Irreducible and Prime Elements
PID implies UFD
The Minimal Polynomial
Kronecker's Theorem
Existence of Splitting Fields
Homework 4
Solutions in the Notes
Mon Apr 1 Working With Irreducible Polynomials
Cyclotomic Polynomials
Existence and Uniqueness of Finite Fields
Fundamental Theorem of Algebra
Exam 2
Solutions
Fri Apr 5
Homework 5
Fri Apr 26 The Finiteness Theorem
The Splitting Field Theorem
Artin's Fixed Field Lemma
Characterization of Galois Extensions
The Fundamental Theorem of Galois Theory