Course Information
SemesterCourse Unit CodeCourse Unit TitleL+PCreditNumber of ECTS Credits
5MATH389INTRODUCTION TO COMMUTATIVE RING THEORY 3+036

Course Details
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. Zero-divisors, 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 co-requisities 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

Course Category

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
In-Term Studies Quantity Percentage
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 Quantity Duration 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:
NoLearning 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
WeekTopicsStudy MaterialsMaterials
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 Zero-divisors, 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
P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11 P12 P13 P14
C1 4 4 4 4 4
C2 4 4 4 4 4
C3 4 4 4 4 4
C4 4 4 4 4 4

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