Semester  Course Unit Code  Course Unit Title  L+P  Credit  Number of ECTS Credits 
5  MATH389  INTRODUCTION TO COMMUTATIVE RING THEORY  3+0  3  6 
Language of Instruction

English

Level of Course Unit

First Cycle

Department / Program

MATHEMATICS

Mode of Delivery

Face to Face

Type of Course Unit

Elective

Objectives of the Course

This course aims to study commutative ring theory.

Course Content

Definition of Rings, Ideals and examples. Prime and Maximal ideals. Ring Homomorphisms. Factor rings and Isomorphism Theorems. Zerodivisors, invertible elements and nilpotent elements. Prime radical of a ring. Jacobson radical of a ring. Rings with descending chain conditions. Rings with ascending chain conditions. Examples of rings with chain conditions.

Course Methods and Techniques


Prerequisites and corequisities

None

Course Coordinator

None

Name of Lecturers

Prof.Dr. Engin Büyükaşık enginbuyukasik@iyte.edu.tr

Assistants

None

Work Placement(s)

No

Recommended or Required Reading
Resources

Rings and Their Modules, P.E. Bland Steps in Commutative Algebra, R.Y. Sharp Introduction to Commutative Algebra, M. Atiyah










Planned Learning Activities and Teaching Methods
Activities are given in detail in the section of "Assessment Methods and Criteria" and "Workload Calculation"
Assessment Methods and Criteria
InTerm Studies

Midterm exams

2

%
60

Quizzes

0

%
0

Homeworks

0

%
0

Other activities

0

%
0

Laboratory works

0

%
0

Projects

0

%
0

Final examination

1

%
40

Total

3

%
100

ECTS Allocated Based on Student Workload
Activities

Total Work Load

Weekly Course Time

3

14

42

Outside Activities About Course (Attendance, Presentation, Midterm exam,Final exam, Quiz etc.)

5

14

70

Exams and Exam Preparations

6

12

72

Total Work Load
 

Number of ECTS Credits 6
184

Course Learning Outcomes: Upon the successful completion of this course, students will be able to:
No  Learning Outcomes 
1
 Rings and their ideals should be known. 
2
 Factor rings and isomorphism theorems should be known. 
3
 Prime and Jacobson radical of a commutative ring should be known. 
4
 Basic facts for rings with chain conditions should be known. 
Weekly Detailed Course Contents
Week  Topics  Study Materials  Materials 
1 
Definition of Rings



2 
Ideals and examples



3 
Prime and Maximal ideals



4 
Ring Homomorphisms



5 
Factor rings and Isomorphism Theorems



6 
Midterm Exam



7 
Zerodivisors, invertible elements and nilpotent elements



8 
Prime radical of a ring



9 
Jacobson radical of a ring



10 
Review



11 
Midterm Exam



12 
Rings with descending chain conditions



13 
Rings with ascending chain conditions



14 
Examples of rings with chain conditions



Contribution of Learning Outcomes to Programme Outcomes
Contribution: 0: Null 1:Slight 2:Moderate 3:Significant 4:Very Significant
https://obs.iyte.edu.tr/oibs/bologna/progCourseDetails.aspx?curCourse=227345&lang=en