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HIGHER ALGEBRA 2

CODE 42911
ACADEMIC YEAR 2018/2019
CREDITS 7 credits during the 1st year of 9011 Mathematics (LM-40) GENOVA
SCIENTIFIC DISCIPLINARY SECTOR MAT/02
LANGUAGE Italian (English on demand)
TEACHING LOCATION GENOVA (Mathematics)
SEMESTER 2° Semester
TEACHING MATERIALS AULAWEB

OVERVIEW

Language: Italian

This is a course on Commutative Algebra, and will be centered on the issue of the lack of bases for modules over a ring: most modules are not free, so one has to "approximate" them in some way. The better is the approximation, the better is the ring, in a sense that agrees with the geometric concept of singularities: we will see in detail regular ring, Cohen-Macaulay rings, UFD's, techniques from homological algebra

AIMS AND CONTENT

LEARNING OUTCOMES

Provide students with the basics of homologous algebra and notions such as free resolution and depth of a module; Introduce / deepen regular rings, Cohen-Macaulai rings, and UFDs.

TEACHING METHODS

Teaching style: In presence

SYLLABUS/CONTENT

Homological algebra. Hilbert functions. Regular sequences. Grade and depth. The Koszul complex. Free resolutions. Regular rings. Cohen-Macaulay rings. Complete intersections. Gorenstein rings. Canonical modules and local cohomology. Stanley Reisner rings, determinanntal rings. 

TEACHERS AND EXAM BOARD

Exam Board

MATTEO VARBARO (President)

EMANUELA DE NEGRI

MARIA EVELINA ROSSI

LESSONS

TEACHING METHODS

Teaching style: In presence

LESSONS START

The class will start according to the academic calendar.

Class schedule

All class schedules are posted on the EasyAcademy portal.

EXAMS

EXAM DESCRIPTION

Oral.

Exam schedule

Date Time Location Type Notes
21/02/2019 10:00 GENOVA Orale
13/06/2019 10:00 GENOVA Scritto
08/07/2019 10:00 GENOVA Orale