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KnowledgeOn successful completion of the module, students should be able to: - know the basic concepts and constructions in commutative algebra, such as ideals, modules, exact sequences, tensor products, localization, primary decompositions, Artinian and Noethian rings and modules, Gröbner bases and computations on polynomial rings; - prove any of the theorems given in the course; - deduce properties which follow from these theorems; - prove other algebraic results using rigorous arguments; - demonstrate their mastery by solving non-trivial problems related to these concepts; - have a geometric viewpoint on the subject as preparation for a future topics course on algebraic geometry.
Assessment criteria of knowledgeIn the written exam, the student must demonstrate his/her mastery in the course material by solving non-trivial problems. In the oral exam the student will be assessed on his/her demonstrated ability to discuss the main course contents using the appropriate terminology.
- Final oral exam
- Final written exam
- Periodic written tests
Delivery: face to face
- attending lectures
- individual study
SyllabusCommutative rings, modules, tensor products, localization, primary decomposition, Noetherian and Artinian ring and modules. Polynomial rings and Groebner bases.
BibliographyRecommended reading: M. F. Atiyah, I.G. Macdonald, "Introduction to Commutative Algebra" D.Cox, J.Little, D.O'Shea, ``Ideals, Varieties and Algorithms'' H. Matsumura, ``Commutative Ring Theory'' D.Eisenbud, ``Commutative Algebra with a view toward Algebraic Geometry'' M.Reid, ``Undergraduate Commutative Algebra''
Ultimo aggiornamento 14/11/2016 17:27