| First cycle degree courses | Second cycle degree courses | Single cycle degree courses |
| School of Science | ||
| MATHEMATICS | ||
Course unit
RINGS AND MODULES
SCL1001443, A.A. 2019/20
Information concerning the students who enrolled in A.Y. 2019/20
RINGS AND MODULES
SCL1001443, A.A. 2019/20
Information concerning the students who enrolled in A.Y. 2019/20
Information on the course unit
| Degree course |
Second cycle degree in MATHEMATICS SC1172, Degree course structure A.Y. 2011/12, A.Y. 2019/20 |
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|---|---|---|
| Degree course track | GENERALE [010PD] | |
| Number of ECTS credits allocated | 6.0 | |
| Type of assessment | Mark | |
| Course unit English denomination | RINGS AND MODULES | |
| Website of the academic structure | http://matematica.scienze.unipd.it/2019/laurea_magistrale | |
| Department of reference | Department of Mathematics | |
| Mandatory attendance | No | |
| Language of instruction | English | |
| Branch | PADOVA | |
| Single Course unit | The Course unit can be attended under the option Single Course unit attendance | |
| Optional Course unit | The Course unit can be chosen as Optional Course unit |
Lecturers
| Teacher in charge | SILVANA BAZZONI | MAT/02 |
|---|
Mutuated
| Course unit code | Course unit name | Teacher in charge | Degree course code |
|---|---|---|---|
| SCL1001443 | RINGS AND MODULES | SILVANA BAZZONI | SC1172 |
ECTS: details
| Type | Scientific-Disciplinary Sector | Credits allocated | |
|---|---|---|---|
| Core courses | MAT/02 | Algebra | 6.0 |
Course unit organization
| Period | Second semester |
|---|---|
| Year | 1st Year |
| Teaching method | frontal |
| Type of hours | Credits | Teaching hours |
Hours of Individual study |
Shifts |
|---|---|---|---|---|
| Practice | 2.0 | 16 | 34.0 | No turn |
| Lecture | 4.0 | 32 | 68.0 | No turn |
| Start of activities | 02/03/2020 |
|---|---|
| End of activities | 12/06/2020 |
| Show course schedule | 2019/20 Reg.2011 course timetable |
| Prerequisites: | Notions from the Algebra courses of the first two years of the degree in Mathematics and basic notions on module theory over arbitrary rings. |
| Target skills and knowledge: | The aim of the course is to learn the basic notions in catgeory theory and the related main constructions. To introduce the techniques and the tools of homological algebra and their applications to dimension theory. |
| Examination methods: | Written exam consisting in answering to questions from the theory and in solving exercises.
Discussion of the composition and possible oral exam. |
| Assessment criteria: | Check of the learning of the taught notions and on the ability of their application. |
| Course unit contents: | Additive and Abelian categories. Functor categories. Freyd-Mitchell embedding theorem. Pull-back and push-out. Limits and colimits. Adjoint functors. Categories of chain complexes and the homotopy category. Foundamental Theorem in homology. Left and right derived functors. The functors Tor, flatness and purity. The funtors Ext and Yoneda extensions. Flat, projective and injective dimensions of modules and their characterization in terms of derived functors. Applications to the global dimension of rings and Hilbert's syzygies Theorem. |
| Planned learning activities and teaching methods: | Lists of exercises to solve will be distributed to check and to deepen the learning of the taught notions.
The notes of the lectures will be distributed daily. |
| Additional notes about suggested reading: | Notes of the lectures, solving of the proposed exercises. Reading of the books in the bibliography. |
| Textbooks (and optional supplementary readings) |
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