Introdurre alle nozioni basilari di algebra commutativa necessarie per lo studio della Geometria Algebrica.
---------------------------------------
Commutative Algebra studies commutative rings (with identity), their ideals, and modules based on such rings. Both algebraic geometry and algebraic number theory are based on commutative algebra. We start from the basic notions (ideals, polynomial rings, multiplicatively closed subsets and localizations) up to Noetherian rings and modules, Krull’s Theorem, Hilbert’s Nullstellensatz and dimension theory.
Algebra e geometria del biennio della Laurea.
---------------------------------------
Basic notions of algebra and geometry.
Italiano
Lezioni frontali in lingua inglese.
---------------------------------------
English Classroom Lectures.
1) M.F. Atiyah & I.G. MacDonald, Introduction to Commutative Algebra, Addison-Wesley 1969 (ed. Feltrinelli, 1981)
2) H. Matsumura, Commutative Ring Theory, Cambridge University Press, 1986
1. anelli, ideali, moduli, polinomi e localizzazione
2. decomposizione primaria e spettro primo di un anello
3. Hilbert’s Nullstellensatz
4. teoria della dimensione, metodi omologici e anelli regolari
---------------------------------------
1. rings, ideals, modules, polynomials and localizations
2. primary decomposition and the prime spectrum of a ring
3. Hilbert’s Nullstellensatz
4. dimension theory, homological methods and regular rings
D. Eisenbud, Commutative Algebra with a view toward Algebraic Geometry Vol. 150 of Graduate Texts in Math. Berlin, Springer-Verlag, 1994.