A.Facchini
Rings and Modules 1 (Anelli e moduli 1)
University of Padova, Italy
Faculty of di Mathematics, Physics and Natural Sciences Mathematics Second Level Course
It is open to students of the Master’s degree in Mathematics (Laurea Specialistica), and bachelor’s degree in Mathematics (Laurea triennale) and to students of the Master Mundus ALGANT program.
When: second trimester
Where: Department of Pure and Applied Maths, Padova.
Total number of hours: about 48 (6 credits).
Examination: oral.
Description of the course
This is a first course about the so-called “rings with several objects”. It is very impor- tant that the student already has a knowledge of what has been done in the previous course
“Introduction to Ring Theory” (Introduzione alla Teoria degli Anelli).
Program Semisimple artinian rings
Maschke’s Theorem Jacobson radical
Hereditary rings, Dedekind rings, projective dimension Tensor product, flat modules
Local rings
Injective modules, essential extensions Injective dimension
Graded modules
Complexes, homology groups Derived functors
Tor and Ext
References
Donald S. Passman A Course in Ring Theory, AMS Chelsea Publishing, Providence, Rhode Island, 2004.