Algebra (2017/2018)

Course code
Lidia Angeleri
Other available courses
Other available courses
    Academic sector
    MAT/02 - ALGEBRA
    Language of instruction
    Teaching is organised as follows:
    Activity Credits Period Academic staff Timetable
    Elementi di algebra 6 I sem. Lidia Angeleri, Giovanni Zini

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    Teoria di Galois 3 I sem. Lidia Angeleri, Giovanni Zini

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    Learning outcomes

    The course provides an introduction to modern algebra. After presenting and discussing the main algebraic structures (groups, rings, fields), the focus is on Galois theory. Also some applications are discussed, in particular results on solvability of polynomial equations by radicals.


    Elements of Algebra:
    Groups, subgroups, cosets, quotient groups. Solvable groups. Sylow's theorems. Rings. Ideals. Homomorphisms. Principal ideal domains. Unique factorization domains. Euclidean rings. The ring of polynomials. Fields. Algebraic field extensions. The splitting field of a polynomial. Finite fields. Constructions with ruler and compass.
    Galois Theory:
    Separable extensions. Galois theory. Theorem of Abel-Ruffini.

    Prerequisites: Linear Algebra

    Assessment methods and criteria

    The exam consists of a written examination. The mark obtained in the written examination can be improved by the mark obtained for the homework and/or by an optional oral examination. Only students who have passed the written exam will be admitted to the oral examination.

    Reference books
    Activity Author Title Publisher Year ISBN Note
    Elementi di algebra S. Bosch Algebra Springer Unitext 2003 978-88-470-0221-0
    Elementi di algebra I. N. Herstein Algebra Editori Riuniti 2003