Information Package / Course Catalogue
Introduction to Gamma Rings
Course Code: MTK579
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 course aims to introduce and to understand the definition and fundamental notions of gamma rings which is the generalization of usual rings and the course aims to give information about the structure of gamma rings.

Course Content

Definition of a gamma ring and examples, operator rings, the notion of an ideal and homomorphism, primeness, primitivity, simpleness, density theorem, prime radical, Levitzki nil radical, Jacobson radical.

Name of Lecturer(s)
Lec. Okan ARSLAN
Learning Outcomes
1.Ability to understand the notion and fundamental properties of gamma ring, and to learn examples of some gamma rings.
2.Ability to understand the operator rings and its fundamental properties of a gamma ring.
3.Ability to know about the relations between operator rings and gamma rings.
4.Ability to determine the information about the structure of a gamma ring.
5.Ability to know about the radicals of a gamma ring.
Recommended or Required Reading
1.Gamma Rings, S. Kyuno, Hadronic Press Inc., Palm Habor, 1991.
Weekly Detailed Course Contents
Week 1 - Theoretical
Definition of gamma ring and some examples of gamma rings
Week 2 - Theoretical
Mutual relations of various gamma rings
Week 3 - Theoretical
Operator rings of gamma rings
Week 4 - Theoretical
Ideals and homomorphisms of gamma rings
Week 5 - Theoretical
Residue class gamma rings
Week 6 - Theoretical
Notion of primeness of gamma rings
Week 7 - Theoretical
Notion of primitivity of gamma rings
Week 8 - Theoretical
Notion of simpleness of gamma rings
Week 9 - Theoretical
Density theorem for gamma rings
Week 10 - Theoretical
Prime radical of gamma rings
Week 11 - Theoretical
Levitzki nil radical of gamma rings
Week 12 - Theoretical
Jacobson radical of gamma rings
Week 13 - Theoretical
Relations among radicals of gamma rings and operator rings
Week 14 - Theoretical
Relations among the various radicals of gamma rings
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
4
4
4
OÇ-2
3
3
4
OÇ-3
4
4
3
OÇ-4
4
3
3
OÇ-5
3
4
4
Adnan Menderes University - Information Package / Course Catalogue
2026