Courses:

Math 8250 T Th 2:30-3:45pm

Lecture notes:

Lecture 1: Flatness and completion;
Lecture 2: I-adic completion, Artin-Rees lemma;
Lecture 3: Krull's Theorem;
Lecture 4: Going-down theorem and normal rings;
Lecture 5: Affine domains, valuation rings;
Lecture 6: Characterization of normal rings, Dedekind rings;
Lecture 7: Graded rings and modules, the Hilbert function;
Lecture 8; The Hilbert polynomial, the Hilbert-Samuel function and polynomial;

Math 8240 M W 2:00-3:15pm Syllabus

Lecture notes:

Lecture 1: Polynomial rings, Grobner bases;
Lecture 2: Noetherian and Artinian ring and modules;
Lecture 3: Krull's Intersection Theorem;
Lecture 4: Artinian rings ;
Lecture 5: Finite length modules ;
Lecture 6: Rings of fractions ;
Lecture 7: Modules of fractions;
Lecture 8: Associated primes and the prime filtration;
Lecture 9: Primary decomposition;
Lecture 10: Affine algebraic geometry;
Lecture 11: Affine algebraic geometry II;
Lecture 12: Integral extensions;
Lecture 13: Integral extensions, Noether normalization, Nullstellensatz;

Math 7610 GOML only: Problem Solving Strategies

Past courses

Math 4442/6442 Modern Algebra II Tu Th 1-2:15pm Syllabus

Math 4441/6441 Modern Algebra I MW 3-4:15pm Syllabus

Math 7610 (GOML): Problem Solving Strategies.

Math 8220 Abstract Algebra I MW 1:30-2:45pm Syllabus

Courses for Spring 2012:

Math 8221 Abstract Algebra II Tu Th 4-5:15pm Syllabus

Courses for Fall 2012:

Math 4441/6441 Modern Algebra I MW 12-1:15pm Syllabus

Math 8220 Abstract Algebra I MW 1:30-2:45pm Syllabus

HON 1000 Tu 10:00-10:50am Syllabus

Commutative Algebra Lectures

These lectures are based upon a two semester course at Georgia State University: Math 8240 (Spring 2010) and Math 8250 (Fall 2010). They represent a preliminary version of the notes. They will undergo revisions periodically.

Math 8240

Math 8250

Lecture 14;
Lecture 15 (revised 10/11/2010);
Lecture 16;
Lecture 17;
Lecture 18;
Lecture 19;
Lecture 20;
Lecture 21;

Courses for Fall 2010:

Math 4444/6444 Polynomials 2:30-3:45pm Syllabus

Lecture 1;
Lecture 2;
Lecture 3;
Lecture 4;
Lecture 5;
Lecture 6;
Lecture 7;
Lecture 8;
Lecture 9;
Lecture 10;
Lecture 11;
Lecture 12;
Homework 1; Solutions Homework 1;
Homework 2; Solutions Homework 2;
Homework 3; Solutions Homework 3;
Homework 4; Solutions Homework 4;
Homework 5; Solutions Homework 5;
Homework 6; Solutions Homework 6;

Courses for Summer 2010:

Math 4441/6441 Modern Algebra I M W F 12:00-1:50pm

Math 1101 Intro to math modeling 10-10:50am


Courses for Summer 2009:

Math 4441/6441 Modern Algebra I M W F 12:00-1:50pm


Courses for Spring 2009:

Math 8221 Abstract Algebra II Tu Th 4:00-5:15pm Syllabus

Math 8801 Research topics in algebra

Courses for Fall 2008:

Math 8220 Tu Th 4:00-5:15pm

Math 4441/6441-Modern Algebra I MW 12-1:15pm Syllabus

Hon 1000 Freshman Honors Seminar Tu 11-11:50am Syllabus

Algebra Qualifying Examination - GSU Ph. D program

List of topics Topics

List of review problems Problems

Recent exams 2009 ; 2010 ; 2011