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KnowledgeThe students are expected to deal with the basic algebraic structures like groups, rings, fields and with an introduction to the Galois theory. They will be tested on the basis of various exercises and examples.
Assessment criteria of knowledgeThe students is asked to solve a number of problems in the written exam and to give proofs and examples relative to the matter of the course.
- Final oral exam
- Final written exam
- Periodic written tests
No special weighting, but roughly 50% is assigned to the written exam and roughly 50% to the oral exam.
Delivery: face to face
- attending lectures
- individual study
- group work
- Task-based learning/problem-based learning/inquiry-based learning
SyllabusTheory of groups : subgroups and normal subgroups, homomorphisms, quotients. Authomorphims, conjugacy classes, class formula, permutations, finite abelian groups. Theory of rings: domains, zero divisors, units, ideals, quotients, homomorphisms. Special rings: euclidean domanins, principal ideal domains, unique factorization domains. Extensions of fields, splitting field of a polynomial, finite Galois theory.
BibliographyRecommended readings include the following books: S. Lang, Undergraduate Algebra 2nd Ed., Springer-Verlag. N. Herstein, Algebra, Editori Riuniti. M. Artin, Algebra, Bollati Boringhieri.
Ultimo aggiornamento 14/11/2016 17:27