Akademik Dersler - Tanıtım


Code - Course Title	MAT551 - Ring and Module Theory
Course Type	Elective Courses
Language of Instruction	Türkçe
Laboratory + Practice	3+0
ECTS	7.5
Course Instructor(s)	PROFESÖR DOKTOR FİGEN TAKIL MUTLU
Mode of Delivery	Face to face
Prerequisites	There is no prerequisite or co-requisite for this course.
Courses Recomended	MAT 519 Algebra
Required or Recommended Resources	1. Kasch, F., Modules and Rings, Academic Press (1982)2. Wisbauer, R, Foundations of Module and Ring Theory, Gordon and Breach Science Publishers (1991)
Recommended Reading List
Assessment methods and criteria	1 Midterm exam, 1 Final exam
Work Placement
Sustainability Development Goals

Weeks	Topics
Week - 1	Modules, Submodules and Ideals
Week - 2	Intersection and Sum of Submodules., Factor Modules, Factor Rings
Week - 3	Module and Ring Homomorphisms, Generators and Cogenerators.
Week - 4	Factorization of Homomorphisms, The Jordan-Hölder-Schreirer Theorem.
Week - 5	The Endomorphism Ring of a Module, Exact Sequences.
Week - 6	Construction of Products and Coproducts, Connection Between the Internal and External Direct Sums, Homomorphisms of Direct Products and Direct Sums.
Week - 7	Free Modules, Divisible Abelian Groups, A characterization of Generators and Cogenerators.
Week - 8	Large and Small Modules, Complements, Definition of Injective and Projective Modules and Simple Corollaries.
Week - 9	Projective Modules, Injective Modules, Injective Hulls and Projective Covers.
Week - 10	Baer's Criteria, Further Characterizations and Properties of Generators and Cogenerators.
Week - 11	Definition of Artinian and Noetherian Modules and Examples.
Week - 12	The Hilbert Basis Theorem, Endomorphisms of Artinian and Noetherian Modules.
Week - 13	Characterizations of Noetherian Rings,
Week - 14	Decompositions of Injective Modules over Noetherian and Artinian Rings.

Assessment Method and Passing Requirements
	Quamtity	Percentage (%)
2.Midterm Exam	1	40
Final Exam	1	60
Toplam (%)		100