Academic year2016/17
CourseMATHEMATICS
Code134AA
Credits9
PeriodSemester 1
LanguageItalian
| Modules | Area | Type | Hours | Teacher(s) |
| ISTITUZIONI DI ALGEBRA | MAT/02 | LEZIONI | 63 | |
Programma non disponibile nella lingua selezionata
Knowledge
The student who successfully completes the course will will be aware of
integral extensions of rings and of dimension theory of local noetherian rings. He/she will know what is a completion of a ring or of a module, he/she will be aware of the relations of commutative algebra with algebraic geometry;
The student will also know what is a category and a functor and will be able to work with some of the most important functors in homological algebra and algebraic topology, i.e. the derived functors Tor^n and Ext^n. he will be able to compute the cohomology of some groups.
Assessment criteria of knowledge
During the oral exam the student must be able to demonstrate his/her knowledge of the course material and be able to discuss the reading matter thoughtfully and with propriety of expression.
Methods:
- Final oral exam
- Final written exam
- Periodic written tests
Teaching methods
Delivery: face to face
Learning activities:
- attending lectures
- preparation of oral/written report
Attendance: Advised
Teaching methods:
Syllabus
First part:
commutative algebra: integral extensions of rings, dimension theory of local noetherian rings, completions,relations with algebraic geometry;
Second part:
homological algebra: injective modules, projective modules, extensions, some notions on categories, functors, derived functors (examples of Tor^n and Ext^n), cohomology of groups with local coefficients.
Bibliography
Recommended reading includes the following works:
Atiyah-MacDonald, Introduction to Commutative Algebra,
Hilton-Stammbach, Homological Algebra.
Further bibliography will be indicated.
Updated: 14/11/2016 17:27
