Ring Theory

Fall semester 2023
Course: MATH 4320 (Undergraduate), MATH 6321 (Graduate)
Course record number: 79527 (Undergraduate), 79128 (Graduate)
Instructor: Y. Sommerhäuser
Schedule:
- Time: Tue, Thu 10:30 am-11:45 am
- Room: HH 3015
Office hours of Y. Sommerhäuser: Mon 11:15 am-12:15 pm, Tue 12:15 pm-1:15 pm, Thu 12:15 pm-1:15 pm, Fri 11:15 am-12:15 pm, and by appointment
Textbook: B. Farb/R. K. Dennis: Noncommutative Algebra, Grad. Texts Math., Vol. 144, Springer, Berlin, 1993 (required resource)
Outline: The course discusses factorization in integral domains, the structure theorem for finitely generated modules over a principal ideal domain, artinian and noetherian rings, Wedderburn-Artin theory, Jacobson radical theory, prime and primitive rings, perfect and semiperfect rings, as well as injective, projective and flat modules. For topics not covered in the textbook, handouts from other sources will be provided.
Examinations: There will be a midterm examination and a comprehensive final examination. The midterm examination takes place on Tuesday, October 17, during regular class time in our usual classroom. The final examination takes place on Thursday, December 7, from 9:00 am to 12:00 m, also in our usual classroom.
Homework: Beginning Tuesday of the second week, a weekly exercise sheet will be handed out. This has to be submitted in class on the following Tuesday. There will be no exercise sheet during the week of the midterm examination and no exercise sheets during the last two weeks of the semester. In addition, a reading assignment from the textbook will be given in almost every lecture.
Writing assignments: To distinguish the graduate course from the undergraduate course, the graduate course will have two additional writing assignments. They will be based on chapters of the textbook that were not covered in class and should be written as an essay of about five to ten pages. They must not repeat the textbook verbatim, but rather be independent expositions without literal quotations. The precise description of the first writing assignment will be given out on Thursday, October 19, and the precise description of the second writing assignment will be given out on Thursday, November 16.
Prerequisites: MATH 3320 (Abstract Algebra) or equivalent
Examination criteria: The final mark will be computed using the following weights.
- Homework: 25 percent
- Midterm examination: 25 percent
- Final examination: 50 percent
Policies: Eating, drinking, and smoking is not permitted in the classroom. You are expected to be present at every class meeting, from the beginning to the end. The use of electronic devices, especially cellphones, calculators, and laptop computers, is not permitted without explicit permission of the instructor. Electronic devices have to be turned off completely.
Syllabus.
Exercise sheets:

Former courses
Last modified: November 29, 2023