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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

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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.

Riferimenti

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