Professor John Beachy, Watson 355, 753-6753
Office Hours: 10:00 - 10:50 (in Watson 355), or by appointment
email: beachy@math.niu.edu | My faculty homepage | My personal homepage
Syllabus | Lecture Schedule | Resources on the WEB
Assignments | Class notes | Homework hints
PREREQUISITE: MATH 520 or consent of department
TEXT: Introductory Lectures on Rings and Modules, Cambridge University Press, and supplementary lecture notes on commutative rings. Recommended reference: Algebra, by Hungerford
SYLLABUS:
These are the topics listed for the comprehensive exam in algebra.
Rings and Modules:
Modules, simplicity, semisimplicity, chain conditions, tensor products,
Jacobson radical, density theorem, Wedderburn-Artin theorem,
finitely generated modules over a principal ideal domain,
canonical forms.
Unique factorization, Euclidean domains, principal ideal domains,
polynomial rings, maximal, prime, and primary ideals,
Noetherian rings, Hilbert basis theorem, Lasker-Noether decomposition,
integral elements, integral closure, fractional ideals, Dedekind domains.
To prepare for these topics, I plan to cover the following sections of the text. (Chapter 5 is a set of supplementary notes available on the web, and is not included in the published version of the book). The emphasis of the book is on noncommutative rings, and so Chapter 4 covers the representation theory of finite groups as an application of the general theory developed in the previous chapters.
CHAPTER 1: RINGS (62 pages)
CHAPTER 2: MODULES (74 pages)
CHAPTER 3: STRUCTURE OF NONCOMMUTATIVE RINGS (34 pages)
CHAPTER 5: IDEAL THEORY OF COMMUTATIVE RINGS (36 pages)
MONDAY WEDNESDAY FRIDAY M Tu W Th F Week of JAN 2005 1/17 HOLIDAY 1.1 1.2 17 18 19 20 21 1/24 1.2 1.3 1.3 24 25 26 27 28 1/31 1.4 1.5 1.5 FEB 31 1 2 3 4 2/7 2.1 2.1 2.1 7 8 9 10 11 2/14 2.2 2.2 2.3 14 15 16 17 18 2/21 2.3 2.4 2.4 21 22 23 24 25 2/28 2.5 2.5 2.6 MAR 28 1 2 3 4 3/7 MIDTERM 2.6 2.6 7 8 9 10 11 SPRING BREAK 14 15 16 17 18 3/21 2.7 2.7 2.7 21 22 23 24 25 3/28 3.1 3.1 3.1 28 29 30 31 1 4/4 3.2 3.2 3.3 APR 4 5 6 7 8 4/11 3.3 3.3 5.1 11 12 13 14 15 4/18 5.1 5.1 5.2 18 19 20 21 22 4/25 5.2 5.3 5.3 25 26 27 28 29 5/2 5.4 5.4 READING DAY MAY 2 3 4 5 6 5/9 FINAL 9 10 11 12 13 FINAL EXAM: Wednesday, May 11, 8:00-9:50 a.m.
GRADING: Semester grades will be based on 500 points:
MIDTERM: The midterm exam is tentatively scheduled for Monday, March 7.
FINAL: The final exam is scheduled for Wednesday, May 11, 8:00-9:50 a.m.
DUE SECTION PROBLEMS
Class notes: some history, solved problems, etc | Abstract Algebra OnLine
Complete books online:
Elements of Abstract and Linear Algebra, by Edwin Connell
Abstract Algebra: The Basic Graduate Year, by Robert Ash
A Course in Commutative Algebra, by Robert Ash
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