
INTRODUCTION TO RING THEORY
Second cycle degree in MATHEMATICS
Campus:
PADOVA
Language:
English
Teaching period:
First Semester
Lecturer:
ALBERTO FACCHINI
Number of ECTS credits allocated:
8
Prerequisites:

Courses of “Algebra 1” and “Algebra 2”. That is, standard undergraduate Algebra. 
Examination methods:

Oral examination and/or evaluation of the exercises solved by the studnts during the course. 
Course unit contents:

Rings. Categories, functors. Modules and their homomorphisms, bimodules, submodules and quotients. Natural transformations. Sets of generators, maximal submodules, free modules and IBN rings, exact sequences, projective modules, tensor product of modules, projective modules over Z. Subcategories. Simple modules, semisimple modules, noetherian modules, artinian modules, modules of finite composition length. Semisimple artinian rings, artinian rings, the Jacobson radical, local rings, injective modules, projective covers, injective envelopes. 

