McGill University

Department of Mathematics & Statistics

Higher Algebra II

189-571B

Detailed Syllabus



Whereas in the first semester we focussed mainly on group theory, representation theory, and Galois theory, the unifying concept for the second semester will be the theory of rings and modules.


1. Monday January 8 to Friday January 12
Text: Basic Algebra, Chapters I and VIII.
Overview of the course. Basic notions of ring theory. Definitions, some key examples.
Assignment 1 (Due Wednesday, January 24.)


2. Monday January 15 to Friday January 19
Text: Basic Algebra, Chapter VIII.
Commutative rings and their modules.



3. Monday January 22 to Friday January 26
Text: Basic Algebra, Chapter VIII.
Commutative rings and their modules, cont'd.


4. Monday January 29 to Friday February 2
Text: Basic Algebra Chapter VIII.
Dedekind rings.
Assignment 2 (Due Wednesday, February 7.)


5. Monday February 5 to Friday February 9
Text: Basic Algebra, Chapter X.
Dedekind rings, cont's. Modules over non-commutative rings.


6. Monday February 12 to Friday February 16
Text: Advanced Algebra, Chapter II.
Artinian rings. Finite-dimensional semisimple modules over F algebras.
Assignment 3 (Due Wednesday, February 21.)


7. Monday February 19 to Friday February 23
Text: Advanced Algebra, Chapter II.
Wedderburn-Artin ring theory, cont'd.


8. Monday February 26 to Monday March 2.
Text: Advanced Algebra, Chapter III.
The Brauer group.
The Midterm will be held this week, on Wednesday, February 28, at 8:30 AM, in room 920.




Monday March 5 to Friday March 9
Study Break





9. Monday March 12 to Friday March 16
Text: Advanced Algebra, Chapter III.
The Brauer group, cont'd.


10. Monday March 19 to Friday March 23
Advanced Algebra, Chapter VIII
Background for algebraic geometry.


11. Monday March 26 to Friday March 30
Advanced Algebra, Chapter VIII.
Background for algebraic geometry, cont'd.


12. Monday April 2 to Friday April 6
Text: Advanced Algebra, Chapter IX.
The number theory of algebraic curves.


13. Monday April 9 to Friday April 13
Text: Advanced Algebra, Chapter IX.
The number theory of algebraic curves, cont'd.

Practice Final