Information Package / Course Catalogue - Adnan Menderes University

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Introduction to Module Theory

Course Code	: MTK510
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 fundamental concepts of modules

Course Content

To give concept of modules, submodules, sum of submodules and intersection of submodules, to define the generators and cogenerators of modules and to give properties of them, to study constraction of product and coproduct, to introduce small submodule, large submodule and complement submodules and studying related properties, to define injective and projective modules and give some basic facts, to study injective hull and projective covers.

Name of Lecturer(s)

Lec. Berna ARSLAN

Learning Outcomes

1.	To be able to give fundamental properties of module theory
2.	To be able to relate module theory with other fields of algebra
3.	To be able to develop some theoretical approach on module theory
4.	To be able to develop individual work on module theory
5.	To be able to relate module theory with some other fields except algebra

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

Modules, submodules and ideals

Week 2 - Theoretical

Intersection and sum of submodules, internal direct sums

Week 3 - Theoretical

Factor modules and factor rings, ring homomorphisms

Week 4 - Theoretical

Generators and cogenerators, factorization of homomorphisms

Week 5 - Theoretical

The theorem of Joran-Hölder-Schreier, the endomorphism ring of modules

Week 6 - Theoretical

Dual modules, exact sequences

Week 7 - Theoretical

Construction of Products and Coproducts

Week 8 - Theoretical

Direct product and direct sum homomorphisms, free modules

Week 9 - Theoretical

Free and divisible abelian groups

Week 10 - Theoretical

Large and small modules

Week 11 - Theoretical

Complements

Week 12 - Theoretical

Injective and projective modules and some basic results

Week 13 - Theoretical

Injective hulls and projective covers

Week 14 - Theoretical

Baer’s Criterion, properties of generators and cogenerators

Assessment Methods and Criteria

Type of Assessment	Count	Percent
Final Examination	1	%70
Assignment	2	%30

Workload Calculation

Activities	Count	Preparation	Time	Total Work Load (hours)
Lecture - Theory	14	3	3	84
Assignment	2	16	2	36
Individual Work	14	0	2	28
Final Examination	1	50	2	52
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	5		4	4	3	2				4				2
OÇ-2	4	5	4	4	3	3	3				4				4
OÇ-3	4	4	4	5	4	3	4				4				4
OÇ-4	4	4	4	4	5	5	5				4				5
OÇ-5	5	5	4	5	4	3	3				4				5

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