TÜRKÇE
ENGLISH
Information
| Code | MT537 |
| Name | Ring Theory |
| 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
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 | ||