Winter Quarter 2018, Math 220B, Modern Algebra II

Instructor:
A. Agboola
Lecture:
TuTh 9:30am-10:45am, LSB 1101
Office:
6724 South Hall
Office hours:
TuTh 11:30am-12:30pm
Textbooks:
The following two books are required texts for this course (as well as for Math 220C):

David S. Dummit, Richard M. Foote, Abstract algebra, (Third Edition), Wiley (2004).

Serge Lang, Algebra, (Revised Third Edition), Springer (2002).

The following book may also be helpful to you:

M. F. Atiyah, I. G. MacDonald, Introduction to commutative algebra, Westview Press (1994).

Grading and Examination Policy:
There will be one take-home midterm examination. It will be handed out in class on Thursday, February 15th, and will be due in class on Tuesday, February 20th. There will also be a final examination. Precise instructions concerning the midterm and final examinations will be given later.

Homework may be assigned, and some of it may be collected. Your work should be typed neatly in Tex on A4-sized paper.

The final grade for the course will be determined as follows: midterm 40\%, final exam. 60\%. Homework will not count towards the final grade.

PLEASE NOTE THAT NO MAKEUP EXAMINATIONS WILL BE GIVEN IN THIS COURSE.

Course Outline:

We shall aim to cover the following topics. Additional topics will be covered if time permits.

Rings and ideals: Rings and ring homomorphisms. Ideals. Quotient rings, zero divisors, nilpotent elements, units. Prime ideals and maximal ideals. Nilradical and Jacobson radical. Fields of fractions, localisation.

Modules over commutative rings. Homomorphisms, submodules, quotient modules, isomorphism theorems, direct sums. Free modules. Noetherian rings and their finitely generated modules. Hilbert's Basis Theorem.

Bilinear maps and tensor products. Alternating maps and exterior powers. Finitely generated free modules and determinants.