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SUPERIOR ALGEBRA

Academic Year 2018/2019 - 2° Year - Curriculum A
Teaching Staff: Alfio Ragusa
Credit Value: 9
Scientific field: MAT/02 - Algebra
Taught classes: 49 hours
Exercise: 24 hours
Term / Semester:

Learning Objectives

Aim of the course is to give an algebraic knowledg of a medium high level both for knowing complex problems of an algebraic type or to give a scientific equipment propaedeutics to scientific research in the field of Commutative Algebra and Algebraic Geometry.


Course Structure

Fontal lessons with seminars by the students and some days dedicated to exercises.


Detailed Course Content

Teory of modules, questions on Homological Algebra, Tor ed Ext, Exactness criterion, free resolutions, minimal free resolutions, characterization of some classes of rings as Cohen Macaulay, regular rings, Gorenstein, applications (Hilbert, Burch, Buchsbaum-Eisenbud Theorems, Hilbert functions and Betti numbers).


Textbook Information

We will us notes by the teacher which will be available by the students of the course.

Alcuni argomenti si potranno trovare sul testo: D. Eisenbud, Commutative Algebra: With a View Toward Algebraic Geometry

more on I. Kaplansky, Commutative rings.