Chiara NICOTERA | MODULE THEORY
Chiara NICOTERA MODULE THEORY
cod. 0522200020
MODULE THEORY
| 0522200020 | |
| DEPARTMENT OF MATHEMATICS | |
| EQF7 | |
| MATHEMATICS | |
| 2024/2025 |
| YEAR OF DIDACTIC SYSTEM 2018 | |
| SPRING SEMESTER |
| SSD | CFU | HOURS | ACTIVITY | |
|---|---|---|---|---|
| MAT/02 | 6 | 48 | LESSONS |
| Exam | Date | Session | |
|---|---|---|---|
| TEORIA DEI MODULI | 08/01/2025 - 10:00 | SESSIONE DI RECUPERO | |
| TEORIA DEI MODULI | 28/01/2025 | SESSIONE DI RECUPERO | |
| TEORIA DEI MODULI | 19/02/2025 - 10:00 | SESSIONE DI RECUPERO |
| Objectives | |
|---|---|
| THE AIM OF THIS COURSE IS TO DEVELOP THE BASIC PROPERTIES OF THE MODULES OVER AN UNITARY RING. THE STUDENT WILL KNOW THE THEORY OF MODULES OVER A UNIT RING WITH EXAMPLES AND MAIN PROPERTIES. IN PARTICULAR THE PROPERTIES OF SOME RELEVANT CLASSES OF MODULES. THE STUDENT MUST BE ABLE TO RECOGNIZE AND USE THE CLASSES OF MODULES STUDIED. HE/SHE MUST ALSO BE ABLE TO APPLY MODULE THEORY TOOLS TO OTHER AREAS OF MATHEMATICS. TEACHING WILL AIM TO PROMOTE STUDENTS' AUTONOMY OF JUDGMENT SO THAT THEY ARE ABLE TO CRITICALLY ANALYZE THE CONCEPTS STUDIED. STUDENTS WILL BE STRONGLY ENCOURAGED TO TAKE CARE OF THE PRESENTATION SO THAT THEY ARE ABLE TO PRESENT THE ARGUMENTS CLEARLY AND USING APPROPRIATE LANGUAGE. STUDENTS WILL BE ABLE TO IMPROVE AND APPLY THEIR STUDY INDIPENDENTLY. |
| Prerequisites | |
|---|---|
| GOOD KNOWLEDGE OF THE SUBJECTS CONTAINED IN THE COURSES OF ALGEBRA I/II AND ALGEBRA III |
| Contents | |
|---|---|
CATEGORIES AND FUNCTORS. MODULES, HOMOMORPHISMS, EXACT SEQUENCES. PRODUCTS AND COPRODUCTS. SIMPLE MODULES. FREE MODULES. PROJECTIVE AND INJECTIVE MODULES. NOETHERIAN MODULES. ARTINIAN MODULES. TENSOR PRODUCT. MODULES OVER A PRINCIPAL IDEAL DOMAIN. |
| Teaching Methods | |
|---|---|
| LECTURES. ATTENDANCE TO CLASS LESSONS IS STRONGLY RECOMMENDED. |
| Verification of learning | |
|---|---|
| THE AIM OF THE EXAMINATION IS TO EVALUATE THE FAMILIARITY OF THE STUDENT WITH THE THEORY OF MODULES. THE EXAMINATION IS ORAL. THE STUDENT HAS TO TALK ABOUT EXAMPLES AND THE PRINCIPAL PROPERTIES OF SOME CLASSES OF MODULES AND IS HAS TO SOLVE SOME EXERCISES. OPTIONAL IS TO PRESENT A SHORT SEMINAR ON A TOPIC NOT PRESENTED IN THE LECTURES. |
| Texts | |
|---|---|
| M. CURZIO, P. LONGOBARDI, M. MAJ - LEZIONI DI ALGEBRA - LIGUORI EDITORE, NAPOLI, II EDIZIONE 2014. T.W. HUNGERFORT - ALGEBRA - SPRINGER-VERLAG, BERLIN, 1974. T.S. BLYTH - MODULE THEORY - CLARENDON PRESS, OXFORD, 1990. |
| More Information | |
|---|---|
| CNICOTERA@UNISA.IT |
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