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| MAT7244 | Associative algebras | 3+0+0 | ECTS:7.5 | | Year / Semester | Spring Semester | | Level of Course | Third Cycle | | Status | Elective | | Department | DEPARTMENT of MATHEMATICS | | Prerequisites and co-requisites | None | | Mode of Delivery | Face to face | | Contact Hours | 14 weeks - 3 hours of lectures per week | | Lecturer | -- | | Co-Lecturer | Assistant Prof. Dr. Sultan YAMAK | | Language of instruction | Turkish | | Professional practise ( internship ) | None | | | | The aim of the course: | | Advanced algebra and related issues is to provide basic information for those wishing to do research. |
| Programme Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | PO - 1 : | learn the structure of modules | 1,2,5 | 1 | | PO - 2 : | learn the basic features of simple and semisiple algebra | 1,2,5 | 1 | | PO - 3 : | learn the relationship between the radical of an algebra and jacobson radical | 1,2,5 | 1 | | PO - 4 : | learn the basic features of artinian algebra and the structure of ideals in artinian algebra | 1,2,5 | 1 | | PO - 5 : | have deep knowledge about the decomposition of modules | 1,2,5 | 1 | | PO - 6 : | learn the structure of projective modules over artinian algebras and the structure of projective modules | 1,2,5 | 1 | | PO - 7 : | have deep knowledge about the finite representative type | 1,2,5 | 1 | | CTPO : Contribution to programme outcomes, TOA :Type of assessment (1: written exam, 2: Oral exam, 3: Homework assignment, 4: Laboratory exercise/exam, 5: Seminar / presentation, 6: Term paper), PO : Learning Outcome | | |
| The structure of semisimple algebras, The radical, Indecompasable modules, Profevtive modules over artinian algebras, Finite reepresentation type |
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | Modules, The lattice of submodules, | | | Week 2 | Simple and semisimple modules
| | | Week 3 | Semisimple algebras, Simple algebras
| | | Week 4 | The radical of an algebra,Nakayama's lemma
| | | Week 5 | The jacobson radical,The radical of an artinian algebra
| | | Week 6 | Artinian algebras | | | Week 7 | Applications | | | Week 8 | Mid-term exam | | | Week 9 | Nilpotent algebras | | | Week 10 | Ideals in artinian algebras | | | Week 11 | Direct Decompositions,Local algebras, | | | Week 12 | Fitting's lemma,Projektif modüller,Structure of projektif modules | | | Week 13 | Structure of projektif modules | | | Week 14 | Finite representation Type | | | Week 15 | Applications | | | Week 16 | End-of-term exam | | | |
| 1 | Pierce S., R., 1982, Associative Algebras, Springer-Verlag New York Inc. | | | 2 | Bhattacharya, P.B.,Jain, S.K, Nagpaul S.R, 1994, Basic Abstract Algebra, Cabbridge University Press, Second edition. | | | |
| 1 | Hunderford, T.W., 1987, Algebra, Springer-verlag New York. Heidelberk Berlin | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 8 | 31/03/2017 | 2 | 30 | | Quiz | 11 | 13/04/2017 | 2 | 30 | | End-of-term exam | 16 | 26/05/2017 | 2 | 40 | | |
| Student Work Load and its Distribution | | Type of work | Duration (hours pw) | No of weeks / Number of activity | Hours in total per term | | Yüz yüze eğitim | 3 | 14 | 42 | | Sınıf dışı çalışma | 10 | 14 | 140 | | Arasınav için hazırlık | 10 | 2 | 20 | | Arasınav | 2 | 1 | 2 | | Uygulama | 4 | 2 | 8 | | Ödev | 4 | 3 | 12 | | Dönem sonu sınavı için hazırlık | 6 | 1 | 6 | | Dönem sonu sınavı | 2 | 1 | 2 | | Total work load | | | 232 |
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