To show the organization of the course that includes this module, follow this link 
Course organization
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. At the end of the course the student will be expected to demonstrate that s/he has attained adequate skills in synthesis and abstraction, as well as the ability to recognize and produce rigorous proofs and to formalize and solve moderately difficult problems related to the topics of the course.
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MM: Elementi di algebra teoria
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Groups, subgroups, cosets, quotient groups. Cyclic groups. The symmetric group. Sylow's Theorems. Solvable groups. 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.
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MM: Drills on elements of algebra
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MM: Galois theory
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Normal extensions. Separable extensions. Galois theory. Theorem of Abel-Ruffini.
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MM: Drills on Galois theory
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| Author | Title | Publisher | Year | ISBN | Note |
| I. N. Herstein | Algebra | Editori Riuniti | 2003 | ||
| Sigfried Bosch | Algebraic Geometry and Commutative Algebra | Springer | 2013 |
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.
