Winter Quarter 2018, Math 220B, Modern Algebra II
TuTh 9:30am-10:45am, LSB 1101
6724 South Hall
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.
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,
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.