Nevşehir Hacı Bektaş Veli University Course Catalogue

Information Of Programmes

INSTITUTE OF SCIENCE / MAT602 - MATHEMATICS (DOCTORATE DEGREE)

Code: MAT602 Course Title: THEORY OF RING II Theoretical+Practice: 3+0 ECTS: 6
Year/Semester of Study 1 / Spring Semester
Level of Course 3rd Cycle Degree Programme
Type of Course Optional
Department MATHEMATICS (DOCTORATE DEGREE)
Pre-requisities and Co-requisites None
Mode of Delivery Face to Face
Teaching Period 14 Weeks
Name of Lecturer SEZER SORGUN (ssorgun@nevsehir.edu.tr)
Name of Lecturer(s)
Language of Instruction Turkish
Work Placement(s) None
Objectives of the Course
To teach the structure of some rings and develop the knowledges about this subjects.

Learning Outcomes PO MME
The students who succeeded in this course:
LO-1 Can know the structure of different type Rings PO-3 Students will be dominated by current issues in mathematics.
 		Examination
LO-2 Can attain the scientific knowledge and study as independent. PO-1 Students can design an original issue and explore new, different and / or comprehend complex issues.
PO-2 Students will understand all aspects of mathematics and deepen the knowledge level that can innovate in this field.
 		Performance Project
Term Paper
PO: Programme Outcomes
MME:Method of measurement & Evaluation

Course Contents
Modules, Homologie, Euclidean rings, Noetherian Rings, Atrinian Rings, Semisimple Rings, Reduced and Armendariz rings, Baer and quasi-Baer rings, Wedderburn's theorem on finite division rings, Frobenius rings, Quasi-Frobenius rings,Pseudo-Frobenius rings, Ring extensions
Weekly Course Content
Week Subject Learning Activities and Teaching Methods
1 Modules Teaching topic and applications
2 Homologie Teaching topic and applications
3 Euclidean rings Teaching topic and applications
4 Noetherian Rings Teaching topic and applications
5 Atrinian Rings Teaching topic and applications
6 Semisimple Rings Teaching topic and applications
7 Reduced and Armendariz rings Teaching topic and applications
8 mid-term exam
9 Baer and quasi-Baer rings Teaching topic and applications
10 Wedderburn's theorem on finite division rings Teaching topic and applications
11 Frobenius rings Teaching topic and applications
12 Quasi-Frobenius rings Teaching topic and applications
13 Pseudo-Frobenius rings Teaching topic and applications
14 Ring extensions Teaching topic and applications
15 Ring extensions Teaching topic and applications
16 final exam
Recommend Course Book / Supplementary Book/Reading
1 1-Taşçı, D., (2008), Soyut Cebir, Alp yayınları
2 2- Goldstein, I. N., (1973) Abstract Algebra, Prentice Hall, New York
3 3- Passman, D.S., (2004) A course in Ring Theory, AMS Chelsea Publishing
4 4-Fuller F.W., Anderson R., (1974) Rings and Categories of Modules, Springer-Verlag, New York
Required Course instruments and materials
The books of lecture

Assessment Methods
Type of Assessment Week Hours Weight(%)
mid-term exam 8 2 30
Other assessment methods
1.Oral Examination
2.Quiz
3.Laboratory exam
4.Presentation
5.Report
6.Workshop
7.Performance Project 7 2 10
8.Term Paper 14 2 10
9.Project
final exam 16 2 50

Student Work Load
Type of Work Weekly Hours Number of Weeks Work Load
Weekly Course Hours (Theoretical+Practice) 3 14 42
Outside Class
       a) Reading 2 14 28
       b) Search in internet/Library 2 14 28
       c) Performance Project 3 7 21
       d) Prepare a workshop/Presentation/Report 0
       e) Term paper/Project 3 7 21
Oral Examination 0
Quiz 0
Laboratory exam 0
Own study for mid-term exam 3 8 24
mid-term exam 2 1 2
Own study for final exam 3 8 24
final exam 2 1 2
0
0
Total work load; 192