Specialized Topics in Algebra (ΑΛ6): Διαφορά μεταξύ των αναθεωρήσεων
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! Learning outcomes | ! Learning outcomes | ||
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The | The aim of the course is for the postgraduate student to reach a good level of theoretical background on topics related to the theory of commutative rings. | ||
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! General Competences | ! General Competences | ||
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The course | The aim of the course is to empower the postgraduate student to analyse and compose basic notions of Commutative Algebra. | ||
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Αναθεώρηση της 13:27, 24 Νοεμβρίου 2022
Graduate Courses Outlines - Department of Mathematics
General
School | School of Science |
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Academic Unit | Department of Mathematics |
Level of Studies | Graduate |
Course Code | ΑΛ6 |
Semester | 2 |
Course Title | Specialized Topics in Algebra |
Independent Teaching Activities | Lectures (Weekly Teaching Hours: 3, Credits: 7.5) |
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 aim of the course is for the postgraduate student to reach a good level of theoretical background on topics related to the theory of commutative rings. |
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General Competences |
The aim of the course is to empower the postgraduate student to analyse and compose basic notions of Commutative Algebra. |
Syllabus
- Representations and characters of groups.
- Groups and homomorphisms.
- FG-modules και group-algebras.
- Schur’s Lemma and Maschke’s Theorem.
- Group-algebras and irreducible modules.
- Conjugacy classes and characters.
- Character tables and orthogonality relations.
- Normal subgroups and lifted characters.
- Elementary examples of characters tables.
- Tensor products. Restricting representations to subgroups.
- Applications.
Teaching and Learning Methods - Evaluation
Delivery |
Face to face | ||||||||||
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Use of Information and Communications Technology | - | ||||||||||
Teaching Methods |
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Student Performance Evaluation |
The evaluation is based on the combined performance of the graduate student in:
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Attached Bibliography
- Μαλιάκας Μιχάλης, Εισαγωγή στην Μεταθετική Άλεβρα, Εκδόσεις Σοφία, 2008
- Atiyah, M. F.; Macdonald, I. G., Introduction to commutative algebra. Addison-Wesley Publishing Co., 1969 ix+128 pp.