Second Level Degree in Mathematics
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INTRODUCTION TO RING THEORY - 8 CFU
Teacher
Alberto Facchini
Scheduled Period
I Year - 1 Semester | 30/09/2019 - 18/01/2020
Hours: 64 (32 esercitazione, 32 lezione)
Prerequisites
Courses of “Algebra 1” and “Algebra 2”. That is, standard undergraduate Algebra.
Target skills and knowledge
This is a first course about noncommutative rings and modules over noncommutative rings.
Examination methods
Oral examination and/or evaluation of the exercises solved by the studnts during the course.
Assessment criteria
Correctness of answers and solutions.
Course 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.
Planned learning activities and teaching methods
Standar lectures at the blackboard, with exercises (solved in part by the students themseves).
Additional notes about suggested reading
The notes of the course "Introduction to ring theory" are available at the bookshop Libreria Progetto, Via Marzolo 24, Padova. The title is "Introduction to ring and module theory", last edition, 2019.
Textbooks (and optional supplementary readings)
- Alberto Facchini, Introduction to Ring and Module Theory, Padova, Libreria Progetto, 2019. In vendita alla Libreria Progetto, Via Marzolo 2, Padova