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Mathematics (PHD) Main Page / Program Curriculum / Noncommutative Rings and Algebras

Noncommutative Rings and Algebras

Course CodeSemester Course Name LE/RC/LA Course Type Language of Instruction ECTS
DMB0018 Noncommutative Rings and Algebras 3/0/0 DE Turkish 8
Course Goals
To train students in this fundamental area of abstract algebra which is gaining more importance currently due to both applications and theoretical developments.
Prerequisite(s) . Ring Theory
Corequisite(s) -
Special Requisite(s) The minimum qualifications that are expected from the students who want to attend the course.(Examples: Foreign language level, attendance, known theoretical pre-qualifications, etc.)
Instructor(s) Assoc. Prof. Ayten Koç
Course Assistant(s)
Schedule Day, hours, XXX Campus, classroom number.
Office Hour(s) Instructor name, day, hours, XXX Campus, office number.
Teaching Methods and Techniques Formal Lecture
Principle Sources F. W. Anderson, online lecture notes: Lectures on Non-Commutative Rings, 2002.
Other Sources

T.Y. Lam, A first Course in Noncommutative Rings, Springer-Verlag, 1991.

M. Artin, online lecture notes: Noncommutative Rings, 1999.

Course Schedules
Week Contents Learning Methods
1. Week Basics on Rings and Modules Formal Lecture
2. Week Basics on Rings and Modules Formal Lecture
3. Week Projective and Injective Modules Formal Lecture
4. Week Abelian Categories Formal Lecture
5. Week Morita Theory Formal Lecture
6. Week Morita Theory Formal Lecture
7. Week Socle and Radical Formal Lecture
8. Week Noncommutative Localization Formal Lecture
9. Week Noncommutative Localization Formal Lecture
10. Week Examples: Incidence Algebras, Path Algebras, Leavitt Path Algebras, Cluster Algebras Formal Lecture
11. Week Examples: Incidence Algebras, Path Algebras, Leavitt Path Algebras, Cluster Algebras Formal Lecture
12. Week Growth Functions Formal Lecture
13. Week Gelfand-Kirillov Dimension Formal Lecture
14. Week Gelfand-Kirillov Dimension Formal Lecture
15. Week
16. Week
17. Week
Assessments
Evaluation tools Quantity Weight(%)
Midterm(s) 1 30
Homework / Term Projects / Presentations 4 25
Final Exam 1 45


Program Outcomes
PO-1Have ability to develop new mathematical ideas and methods by using high-level mental processes such as creative and critical thinking, problem solving and decision-making.
PO-2Follow the current developments in the field of mathematics, and make the critical analysis, synthesis and evaluation of new and complex ideas.
PO-3Understand the interdisciplinary interaction related to Mathematics and play a role in an effective manner in environments that require with the resolution of problems encountered in this process.
PO-4Defend original views on the discussion of the issues in the field of mathematics with experts and communicate to show competence in oral and written.
PO-5Do research with high-level national and international scientific working groups, and acquire the responsibility to contribute to the literature by publishing original works in respected scientific journals.
PO-6Use computer software to solve problems effectively by following the developments in information and communication technologies.
PO-7Contribute to the solution of social, scientific, cultural and ethical problems encountered issues related to the field and support the development of these values.
PO-8To solve problems related to the field, establish functional interacts by using strategic decision making processes.
PO-9Establish and discuss in written, oral and visual communication at an advanced level by using at least one foreign language.
Learning Outcomes
LO-1I. Develop a deeper understanding of the concepts and methods of modern abstract algebra.
LO-2II. Know fundamental theorems of the subject and outline basic ideas and technics of their proofs.
LO-3III. Apply these theorems and methods.
LO-4IV. Be familiar with important examples that are currently active areas of research.
Course Assessment Matrix:
Program Outcomes - Learning Outcomes Matrix
 PO 1PO 2PO 3PO 4PO 5PO 6PO 7PO 8PO 9