BASICS OF HIGHER ALGEBRA

BASICS OF HIGHER ALGEBRA

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iten
Code
90694
ACADEMIC YEAR
2016/2017
CREDITS
7 credits during the 1st year of 9011 Mathematics (LM-40) GENOVA

7 credits during the 3nd year of 8760 Mathematics (L-35) GENOVA

SCIENTIFIC DISCIPLINARY SECTOR
MAT/02
LANGUAGE
Italiano (Inglese a richiesta)
TEACHING LOCATION
GENOVA (Mathematics)
semester
2° Semester
Teaching materials

OVERVIEW

Language: English

AIMS AND CONTENT

Teaching methods

Teaching style: In presence

SYLLABUS/CONTENT

I - Rings, ideals and modules. Noetherian rings and the Hilbert basis theorem. Polynomials: The ring K [x_1, ..., x_n] of polynomials with coefficientsin a field. Grobner Bases  and the Buchberger algorithm. Systems of polynomial equations and elimination theory.

II - Review of field extensions. Splitting fields of polynomials with coefficients in a field of characteristic 0, normal extensions and their basic properties. Fundamental Theorem of Galois theory. The Galois group of a polynomial. Applications: cyclotomic fields, solvability by radicals of algebraic equations.

TEACHERS AND EXAM BOARD

Exam Board

STEFANO VIGNI (President)

ALDO CONCA (President)

ANNA MARIA BIGATTI (President)

LESSONS

Teaching methods

Teaching style: In presence

LESSONS START

February 27, 2017

ORARI

L'orario di tutti gli insegnamenti è consultabile su EasyAcademy.

Vedi anche:

BASICS OF HIGHER ALGEBRA