Special Topics in Algebra (MAE821)
- Ελληνική Έκδοση
- Undergraduate Courses Outlines
- Outline Modification (available only for faculty members)
General
| School |
School of Science |
|---|---|
| Academic Unit |
Department of Mathematics |
| Level of Studies |
Undergraduate |
| Course Code |
ΜΑE821 |
| Semester |
8 |
| Course Title |
Special topics in Algebra |
| Independent Teaching Activities |
Lectures (Weekly Teaching Hours: 3, Credits: 6) |
| Course Type |
Special Background |
| Prerequisite Courses | - |
| Language of Instruction and Examinations |
Greek |
| Is the Course Offered to Erasmus Students |
Yes (in English) |
| Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
| Learning outcomes |
The basic objective of this lecture is the development of Module Theory. Drawing on this the Theoretical Algebra and deepening it, we will study implications of Theory of Groups and Theory of Rings, that have been studied in previous academic years. This subject consists of two parts. In the first part, after a revision of the basic concepts of the Group Theory and of the Ring Theory, we will define in detail the notion of a module. In the second part, through the Decomposition Theorems we will connect Module Theory with relevant objects, as for example that of the finitely generated groups (achieving the full classification of them) and also with objects of Linear Algebra (through Smith Form, Rational Canonical Form, Jordan Canonical Form). The expectations of the students are to understand the concepts, the definitions and the main theorems of this subject. |
|---|---|
| General Competences |
|
Syllabus
- Rings and Ideals
- Principal Ideal Domains and Unique Factorization Domains
- The notion of Module. Module structure and isomorphism theorems
- Finitely generated modules. Free modules
- Annihilator. Product and direct sum of modules
- Fundamental Structure Theorems
- Vector space decomposition Theorems
- Free torsion modules
- Smith Form. Rational Canonical Form. Jordan Canonical Form.
Teaching and Learning Methods - Evaluation
| Delivery |
Face to face | ||||||||
|---|---|---|---|---|---|---|---|---|---|
| Use of Information and Communications Technology | - | ||||||||
| Teaching Methods |
| ||||||||
| Student Performance Evaluation |
Weakly homeworks and written final examination. |
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus: