
Course unit
INTRODUCTION TO RING THEORY
SC03111812, A.A. 2019/20
Information concerning the students who enrolled in A.Y. 2019/20
ECTS: details
Type 
ScientificDisciplinary Sector 
Credits allocated 
Core courses 
MAT/02 
Algebra 
8.0 
Course unit organization
Period 
First semester 
Year 
1st Year 
Teaching method 
frontal 
Type of hours 
Credits 
Teaching hours 
Hours of Individual study 
Shifts 
Practice 
4.0 
32 
68.0 
No turn 
Lecture 
4.0 
32 
68.0 
No turn 
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 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. 
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

Innovative teaching methods: Teaching and learning strategies
 Lecturing
 Problem solving
Innovative teaching methods: Software or applications used
Sustainable Development Goals (SDGs)

