A. Agboola

TuTh 9:30am-10:45am, LSB 1101

6724 South Hall

TuTh 11:30am-12:30pm

The following two books are required texts for this course (as well as for Math 220C):

David S. Dummit, Richard M. Foote,

Serge Lang,

The following book may also be helpful to you:

M. F. Atiyah, I. G. MacDonald,

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.

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.