RINGS AND MODULES

Second cycle degree in MATHEMATICS

Campus: PADOVA

Language: English

Teaching period: Second Semester

Lecturer: SILVANA BAZZONI

Number of ECTS credits allocated: 6


Syllabus
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.
Examination methods: Written exam with a discussion on the composition.
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.