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


Syllabus
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.