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ISTITUZIONI DI ALGEBRA
|ISTITUZIONI DI ALGEBRA||MAT/02||LEZIONI||63|
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KnowledgeThe student who successfully completes the course will will be aware of integral extensions of rings and of dimension theory of local noetherian rings. He/she will know what is a completion of a ring or of a module, he/she will be aware of the relations of commutative algebra with algebraic geometry; The student will also know what is a category and a functor and will be able to work with some of the most important functors in homological algebra and algebraic topology, i.e. the derived functors Tor^n and Ext^n. he will be able to compute the cohomology of some groups.
Assessment criteria of knowledgeDuring the oral exam the student must be able to demonstrate his/her knowledge of the course material and be able to discuss the reading matter thoughtfully and with propriety of expression.
- Final oral exam
- Final written exam
- Periodic written tests
Delivery: face to face
- attending lectures
- preparation of oral/written report
SyllabusFirst part: commutative algebra: integral extensions of rings, dimension theory of local noetherian rings, completions,relations with algebraic geometry; Second part: homological algebra: injective modules, projective modules, extensions, some notions on categories, functors, derived functors (examples of Tor^n and Ext^n), cohomology of groups with local coefficients.
BibliographyRecommended reading includes the following works: Atiyah-MacDonald, Introduction to Commutative Algebra, Hilton-Stammbach, Homological Algebra. Further bibliography will be indicated.
Ultimo aggiornamento 14/11/2016 17:27