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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)

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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)

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