Information Package / Course Catalogue
Rings and Radicals
Course Code: MTK512
Course Type: Area Elective
Couse Group: Second Cycle (Master's Degree)
Education Language: Turkish
Work Placement: N/A
Theory: 3
Prt.: 0
Credit: 3
Lab: 0
ECTS: 8
Objectives of the Course

The goal of this course is to analyze some properties of rings by using radicals.

Course Content

Rings and ideals, quotients rings and homomorphisms, minimal ve maximal conditions, polynomial rings, nilpotent ideals and classical radical, ideals in semisimple rings, Wedderburn Theorem, modules, definition and properties of Jacobson radical, primitive rings, Levitzki radical, Brown-McCoy radical.

Name of Lecturer(s)
Lec. Okan ARSLAN
Learning Outcomes
1.To be able to illustrate rings and ideals.
2.To be able to list the properties of classical radical.
3.To be able to find the characterization of variable radicals.
4.To be able to apply the ability of abstract thinking to solving problem.
5.To be able to gain the skill of interpreting some interrelations among these concepts.
Recommended or Required Reading
1.Gray, A radical approach to algebra, Addison-Wesley Publishing Company, 1970.
Weekly Detailed Course Contents
Week 1 - Theoretical
Rings and ideals
Week 2 - Theoretical
Qoutients rings and homomorphisms
Week 3 - Theoretical
Minimal ve maximal conditions
Week 4 - Theoretical
Polynomial rings
Week 5 - Theoretical
Nilpotent ideals and classical radical
Week 6 - Theoretical
Ideals in semisimple rings
Week 7 - Theoretical
Wedderburn Theorem
Week 8 - Theoretical
Modules
Week 9 - Theoretical
Definition and properties of the Jacobson Radical
Week 10 - Theoretical
Primitive rings
Week 11 - Theoretical
Structure theorems
Week 12 - Theoretical
Structure theorems
Week 13 - Theoretical
Levitzki radical
Week 14 - Theoretical
Brown-McCoy Radical
Assessment Methods and Criteria
Type of AssessmentCountPercent
Final Examination1%70
Assignment2%30
Workload Calculation
ActivitiesCountPreparationTimeTotal Work Load (hours)
Lecture - Theory143384
Assignment216236
Individual Work140228
Final Examination150252
TOTAL WORKLOAD (hours)200
Contribution of Learning Outcomes to Programme Outcomes
PÇ-1
PÇ-2
PÇ-3
PÇ-4
PÇ-5
PÇ-6
PÇ-7
PÇ-8
PÇ-9
PÇ-10
PÇ-11
PÇ-12
PÇ-13
PÇ-14
PÇ-15
OÇ-1
3
3
3
3
4
OÇ-2
4
4
3
4
4
3
4
OÇ-3
3
4
3
4
4
3
3
OÇ-4
4
4
4
5
OÇ-5
4
4
4
4
3
Adnan Menderes University - Information Package / Course Catalogue
2026