Information Package / Course Catalogue
Advanced Module Theory
Course Code: MTK576
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

This course gives the some special concepts of modules

Course Content

To define Artinian and Noetherian modules and homomorphisms and give some examples of them, to introduce of Hilbert’s Basis Theorem, to study on local rings and local endomorphism rings, to study semisimple modules and semisimple rings, to introduce socle and radical concepts, to give properties of regular and semiperfect rings, to study on Quasi-Frobenius rings.

Name of Lecturer(s)
Learning Outcomes
1.To be able to give basic properties in advanced module theory
2.To be able to relate advanced module theory with related areas in algebra
3.To be able to develop theoretical techniques in advanced algebra
4.To be able to develop individual abilities in advanced algebra
5.To be able to give relations between advanced module theory and related other subject areas
Recommended or Required Reading
1.Moduln und Ringe, F. Kasch, B.G. Teubner Stuttgart 1977.
2.Modules and Rings, F. Kasch, Translated by D.A.R. Wallace, 1982.
3.Rings and Categories of Modules, F.W. Anderson- K.R. Fuller, Springer Verlag 1974
Weekly Detailed Course Contents
Week 1 - Theoretical
Artinian and Noetherian modules
Week 2 - Theoretical
Hilbert’s Basis Theorem
Week 3 - Theoretical
Decomposition of modules over Noetherian and Artinian modules
Week 4 - Theoretical
Local rings, local endomorphism rings
Week 5 - Theoretical
Krull-Remark-Schmidt Theorem
Week 6 - Theoretical
Semisimple modules and rings
Week 7 - Theoretical
Socle and radical
Week 8 - Theoretical
Tensor product and flat modules
Week 9 - Theoretical
Regular rings
Week 10 - Theoretical
Semiperfect modules
Week 11 - Theoretical
Nil ideals and nilpotent ideals
Week 12 - Theoretical
Injectivity and the cogenerator property of ring
Week 13 - Theoretical
Quasi-Frobenius rings and characterization of Quasi- Frobenius rings
Week 14 - Theoretical
Quasi-Frobenius algebras and characterization of Quasi- Frobenius algebras
Week 15 - Theoretical
Final Exam
Assessment Methods and Criteria
Type of AssessmentCountPercent
Assignment2%30
Final Examination1%70
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
4
3
3
OÇ-3
3
4
3
OÇ-4
3
4
3
OÇ-5
4
4
4
Adnan Menderes University - Information Package / Course Catalogue
2026