Course Information
SemesterCourse Unit CodeCourse Unit TitleL+PCreditNumber of ECTS Credits
8MATH444INTRODUCTION TO MODULES AND RINGS3+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 modules and rings.
Course Content Definition of Modules. Submodules and examples, Module Homomorphisms. Direct product and Direct sum of modules. Free and projective modules. Maximal and small submodules Radical of modules
Essential and Simple submodules. Socle of modules. Injective Modules. Injective Hull of Modules
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 Modules and Rings, F. Kasch
Rings and Their Modules, P.E. Bland

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 Modules and submodules should be known.
2 Direct product and direct sum of modules should be known.
3 Projective and injective modules should be known.
4 Socle and Radical of modules should be known.


Weekly Detailed Course Contents
WeekTopicsStudy MaterialsMaterials
1 Definition of Modules
2 Submodules and examples
3 Module Homomorphisms
4 Direct product and Direct sum of modules
5 Free and projective modules
6 Midterm Exam
7 Maximal and small submodules
8 Radical of modules
9 Essential and Simple submodules
10 Socle of modules
11 Review
12 Midterm Exam
13 Injective Modules
14 Injective Hull of Modules


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=227346&lang=en