MT537 Ring Theory

6 ECTS - 3-0 Duration (T+A)- . Semester- 3 National Credit

Information

Code MT537
Name Ring Theory
Term 2024-2025 Academic Year
Semester . Semester
Duration (T+A) 3-0 (T-A) (17 Week)
ECTS 6 ECTS
National Credit 3 National Credit
Teaching Language Türkçe
Level Doktora Dersi
Type Normal
Mode of study Yüz Yüze Öğretim
Catalog Information Coordinator Doç. Dr. ZEYNEP ÖZKURT


Course Goal / Objective

Değişmeli , Değişmeli olmayan Halkalar , Asal , ilkel halkalar, Bölüm halkaları, Lokal halkalar, Goldie halkaları ve temel özelliklerinin incelenmesi

Course Content

Commutative, non-commutrative rings, prime, primitive rings, quotient rings, local rings, goldie rings and key features

Course Precondition

none

Resources

Introduction to Ring Theory Paul M. Cohn

Notes

Steps in Commutative Algebra von R. Y. Sharp


Course Learning Outcomes

Order Course Learning Outcomes
LO01 Know the concept of ideal and section rings.
LO02 Understands the transformations between rings.
LO03 Knows the structure of commutative ring.
LO04 Recognizes the principal ideal, the factorization and Noether rings.
LO05 Understands the structure of non-commutative ring.
LO06 Express the Wedderburn-Artin theorem.
LO07 knows the Jacobson radical theory.
LO08 Understands the structure of prime and primitive rings.
LO09 Understands thequotient rings, Local Rings and Idempotents.
LO10 Comprehend Goldie rings and their properties.


Relation with Program Learning Outcome

Order Type Program Learning Outcomes Level
PLO01 Bilgi - Kuramsal, Olgusal Knows the results of previous research in a special field of mathematics 3
PLO02 Bilgi - Kuramsal, Olgusal Knows in detail the relationship between the results in her area of expertise and other areas of mathematics. 5
PLO03 Bilgi - Kuramsal, Olgusal Establishes new mathematical models with the help of the knowledge gained in the field of specialization. 4
PLO04 Bilgi - Kuramsal, Olgusal Has basic knowledge in all areas of mathematics 5
PLO05 Bilgi - Kuramsal, Olgusal It presents the knowledge gained in different fields of mathematics and their relations with each other in the simplest and most understandable way. 4
PLO06 Bilgi - Kuramsal, Olgusal Effectively uses the technical equipment needed to express mathematics 5
PLO07 Bilgi - Kuramsal, Olgusal Sets up original problems in her field and offers different solution techniques 3
PLO08 Bilgi - Kuramsal, Olgusal It carries out original and qualified scientific studies on the subject related to its field. 4
PLO09 Bilgi - Kuramsal, Olgusal Analyzes existing mathematical theories and develops new theories. 4
PLO10 Beceriler - Bilişsel, Uygulamalı Knows the teaching-learning techniques in areas of mathematics that require expertise and uses these techniques effectively at every stage of education.
PLO11 Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği To have foreign language knowledge at a level to be able to follow foreign sources related to the field and to communicate verbally and in writing with foreign stakeholders.
PLO12 Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği It presents and publishes its original works within the framework of scientific ethical rules for the benefit of its stakeholders.
PLO13 Yetkinlikler - Öğrenme Yetkinliği Adheres to the ethical rules required by its scientific title


Week Plan

Week Topic Preparation Methods
1 Ideal and section rings Study the relevant sections in the book Öğretim Yöntemleri:
Anlatım
2 Transformations between rings Study the relevant sections in the book Öğretim Yöntemleri:
Anlatım
3 Commutative ring Study the relevant sections in the book Öğretim Yöntemleri:
Anlatım
4 Principal ideal and factorization Study the relevant sections in the book Öğretim Yöntemleri:
Anlatım
5 Noether rings Study the relevant sections in the book Öğretim Yöntemleri:
Anlatım
6 Non-commutative ring Study the relevant sections in the book Öğretim Yöntemleri:
Anlatım
7 Wedderburn-Artin theorem Study the relevant sections in the book Öğretim Yöntemleri:
Anlatım
8 Mid-Term Exam Study the relevant sections in the book Ölçme Yöntemleri:
Yazılı Sınav
9 Jacobson Radical theory Study the relevant sections in the book Öğretim Yöntemleri:
Anlatım
10 Perfect ring Study the relevant sections in the book Öğretim Yöntemleri:
Anlatım
11 Artinian ring Study the relevant sections in the book Öğretim Yöntemleri:
Anlatım
12 Hereditary rings Study the relevant sections in the book Öğretim Yöntemleri:
Anlatım
13 Local Rings Study the relevant sections in the book Öğretim Yöntemleri:
Anlatım
14 Idempotents Study the relevant sections in the book Öğretim Yöntemleri:
Anlatım
15 Goldie rings and their properties Study the relevant sections in the book Öğretim Yöntemleri:
Anlatım
16 Term Exams Study the relevant sections in the book Ölçme Yöntemleri:
Yazılı Sınav
17 Term Exams Study the relevant sections in the book Ölçme Yöntemleri:
Yazılı Sınav


Student Workload - ECTS

Works Number Time (Hour) Workload (Hour)
Course Related Works
Class Time (Exam weeks are excluded) 14 3 42
Out of Class Study (Preliminary Work, Practice) 14 5 70
Assesment Related Works
Homeworks, Projects, Others 0 0 0
Mid-term Exams (Written, Oral, etc.) 1 15 15
Final Exam 1 30 30
Total Workload (Hour) 157
Total Workload / 25 (h) 6,28
ECTS 6 ECTS

Update Time: 09.05.2024 11:39