Chiara NICOTERA | MODULE THEORY
Chiara NICOTERA MODULE THEORY
cod. 0522200020
MODULE THEORY
| 0522200020 | |
| DIPARTIMENTO DI MATEMATICA | |
| EQF7 | |
| MATHEMATICS | |
| 2020/2021 |
| YEAR OF COURSE 1 | |
| YEAR OF DIDACTIC SYSTEM 2018 | |
| PRIMO SEMESTRE |
| SSD | CFU | HOURS | ACTIVITY | |
|---|---|---|---|---|
| MAT/02 | 6 | 48 | LESSONS |
| Objectives | |
|---|---|
| THE AIM OF THIS COURSE IS TO DEVELOP THE BASIC PROPERTIES OF THE MODULES OVER AN UNITARY RING. WE WILL ALSO PRESENT SOME RESULTS ON CARDINAL NUMBERS AND CATEGORIES THEORY. AT THE END OF THE COURSE THE STUDENT HAS TO BE ABLE TO APPLY METHODS OF MODULE THEORY TO OTHER AREAS OF SCIENCE. |
| Prerequisites | |
|---|---|
| GOOD KNOWLEDGE OF THE SUBJECTS CONTAINED IN THE COURSES OF ALGEBRA I AND ALGEBRA II |
| Contents | |
|---|---|
| CARDINAL AND ORDINAL NUMBERS. 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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