First cycle
degree courses
Second cycle
degree courses
Single cycle
degree courses
School of Science
MATHEMATICS
Course unit
INTRODUCTION TO RING THEORY
SC03111812, A.A. 2017/18

Information concerning the students who enrolled in A.Y. 2017/18

Information on the course unit
Degree course Second cycle degree in
MATHEMATICS
SC1172, Degree course structure A.Y. 2011/12, A.Y. 2017/18
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Degree course track GENERALE [010PD]
Number of ECTS credits allocated 8.0
Type of assessment Mark
Course unit English denomination INTRODUCTION TO RING THEORY
Website of the academic structure http://matematica.scienze.unipd.it/2017/laurea_magistrale
Department of reference Department of Mathematics
Mandatory attendance No
Language of instruction English
Branch PADOVA
Single Course unit The Course unit can be attended under the option Single Course unit attendance
Optional Course unit The Course unit can be chosen as Optional Course unit

Lecturers
Teacher in charge ALBERTO FACCHINI MAT/02

Mutuated
Course unit code Course unit name Teacher in charge Degree course code
SC03111812 INTRODUCTION TO RING THEORY ALBERTO FACCHINI SC1172

ECTS: details
Type Scientific-Disciplinary Sector Credits allocated
Core courses MAT/02 Algebra 8.0

Mode of delivery (when and how)
Period First semester
Year 1st Year
Teaching method frontal

Organisation of didactics
Type of hours Credits Hours of
teaching
Hours of
Individual study
Shifts
Practice 4.0 32 68.0 No turn
Lecture 4.0 32 68.0 No turn

Calendar
Start of activities 02/10/2017
End of activities 19/01/2018

Examination board
Board From To Members of the board
7 Introduzione alla Teoria degli Anelli - 2017/2018 01/10/2017 30/09/2018 FACCHINI ALBERTO (Presidente)
COLPI RICCARDO (Membro Effettivo)
BAZZONI SILVANA (Supplente)
LUCCHINI ANDREA (Supplente)
TONOLO ALBERTO (Supplente)
6 Introduzione alla Teoria degli Anelli - 2016/2017 01/10/2016 30/11/2017 FACCHINI ALBERTO (Presidente)
COLPI RICCARDO (Membro Effettivo)
BAZZONI SILVANA (Supplente)
LUCCHINI ANDREA (Supplente)
TONOLO ALBERTO (Supplente)

Syllabus
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", Fourth edition, September 2017.
Textbooks (and optional supplementary readings)
  • Alberto Facchini, Introduction to Ring and Module Theory. Padova: Libreria Progetto, 2017. In vendita alla Libreria Progetto, Via Marzolo 2, Padova Cerca nel catalogo