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HIGHER ALGEBRA 1

CODE 39407
ACADEMIC YEAR 2021/2022
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 1° Semester
TEACHING MATERIALS AULAWEB

OVERVIEW

Lectures are in Italian unless students requires otherwise

AIMS AND CONTENT

LEARNING OUTCOMES

Introduction to commutative algebra: noetherian rings, primary decomposition and Krull dimension.

TEACHING METHODS

In presence (accordingly with restrictions due to Covid-19 countermeasures)

SYLLABUS/CONTENT

Rings, Ideal, modules. Rings and modules of fractions. Tensor products of modules. Primary decomposition, integral dependence and valuations, Chain conditions, Noetherian and Artinian rings. Dimension theory. Krullhauptidealssatz.

RECOMMENDED READING/BIBLIOGRAPHY

D. Eisenbud, Commutative Algebra with a View toward algebraic geometry, Springer 1994

Atiyah MacDonald, Introduction to Commutative Algebra, Addison-Weysley 1969.

TEACHERS AND EXAM BOARD

Exam Board

ALESSANDRO DE STEFANI (President)

EMANUELA DE NEGRI

LESSONS

LESSONS START

Accordingly with the academic calendar.

Class schedule

HIGHER ALGEBRA 1

EXAMS

EXAM DESCRIPTION

Oral examination