| Unit | Credits | Academic sector | Period | Academic staff |
|---|---|---|---|---|
| ELEMENTI DI ALGEBRA | 6 | MAT/02-ALGEBRA | II semestre |
Ancora Da Definire
Enrico Gregorio |
| TEORIA DI GALOIS | 3 | MAT/02-ALGEBRA | II semestre |
Ancora Da Definire
Enrico Gregorio |
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: Elementi di algebra esercitazioni
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MM: Teoria di Galois teoria
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Normal extensions. Separable extensions. Galois theory. Theorem of Abel-Ruffini.
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MM: Teoria di Galois esercitazioni
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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.
| Author | Title | Publisher | Year | ISBN | Note |
| I. N. Herstein | Algebra | Editori Riuniti | 2003 | ||
| Sigfried Bosch | Algebraic Geometry and Commutative Algebra | Springer | 2013 |
