Acquire a good knowledge of some methods and fundamental results in the study of the commutative rings and their modules, with
particular reference to the study of ring classes of interest for the algebraic theory of numbers and for algebraic geometry.
particular reference to the study of ring classes of interest for the algebraic theory of numbers and for algebraic geometry.
Curriculum
teacher profile teaching materials
M. Reid, Undergraduate Algebraic Geometry, Cambridge University Press, 1988.
D. Eisenbud, Commutative Algebra with a view toward Algebraic Geometry, Springer-Verlag, 1995.
A. Gathmann, Commutative Algebra, Lecture notes.
Fruizione: 20410445 AL410 - ALGEBRA COMMUTATIVA in Matematica LM-40 CAPORASO LUCIA
Programme
Rings and ideals, maximal ideals and prime ideals, nilradical andJacobson radical, the spectrum of a ring. Modules, finitely generated modules and Nakayama's Lemma, exact sequences, tensor product, restriction and extension of scalars. Rings and modules of fractions, localization. Primary decomposition. Integral dependence and valuation. Chain conditions. Noetherian rings, Hilbert's Basis Theorem, Nullstellensatz. Discrete valuation rings and Dedekind domains. Hints of dimension theory.Core Documentation
M. F. Atiyah, I. G. Macdonald, Introduction to Commutative Algebra. Addison-Wesley, 1996.M. Reid, Undergraduate Algebraic Geometry, Cambridge University Press, 1988.
D. Eisenbud, Commutative Algebra with a view toward Algebraic Geometry, Springer-Verlag, 1995.
A. Gathmann, Commutative Algebra, Lecture notes.
Type of delivery of the course
Frontal lectures, suggested exercises.Type of evaluation
The exam is written and oral. There will be two midterms (that may exempt from the written exam) teacher profile teaching materials
M. Reid, Undergraduate Algebraic Geometry, Cambridge University Press, 1988.
D. Eisenbud, Commutative Algebra with a view toward Algebraic Geometry, Springer-Verlag, 1995.
A. Gathmann, Commutative Algebra, Lecture notes.
Fruizione: 20410445 AL410 - ALGEBRA COMMUTATIVA in Matematica LM-40 CAPORASO LUCIA
Programme
Rings and ideals, maximal ideals and prime ideals, nilradical andJacobson radical, the spectrum of a ring. Modules, finitely generated modules and Nakayama's Lemma, exact sequences, tensor product, restriction and extension of scalars. Rings and modules of fractions, localization. Primary decomposition. Integral dependence and valuation. Chain conditions. Noetherian rings, Hilbert's Basis Theorem, Nullstellensatz. Discrete valuation rings and Dedekind domains. Hints of dimension theory.Core Documentation
M. F. Atiyah, I. G. Macdonald, Introduction to Commutative Algebra. Addison-Wesley, 1996.M. Reid, Undergraduate Algebraic Geometry, Cambridge University Press, 1988.
D. Eisenbud, Commutative Algebra with a view toward Algebraic Geometry, Springer-Verlag, 1995.
A. Gathmann, Commutative Algebra, Lecture notes.
Type of delivery of the course
Frontal lectures, suggested exercises.Type of evaluation
The exam is written and oral. There will be two midterms (that may exempt from the written exam) teacher profile teaching materials
M. Reid, Undergraduate Algebraic Geometry, Cambridge University Press, 1988.
D. Eisenbud, Commutative Algebra with a view toward Algebraic Geometry, Springer-Verlag, 1995.
A. Gathmann, Commutative Algebra, Lecture notes.
Fruizione: 20410445 AL410 - ALGEBRA COMMUTATIVA in Matematica LM-40 LELLI CHIESA MARGHERITA
Programme
Rings and ideals, maximal ideals and prime ideals, nilradical andJacobson radical, the spectrum of a ring. Modules, finitely generated modules and Nakayama's Lemma, exact sequences, tensor product, restriction and extension of scalars. Rings and modules of fractions, localization. Primary decomposition. Integral dependence and valuation. Chain conditions. Noetherian rings, Hilbert's Basis Theorem, Nullstellensatz. Discrete valuation rings and Dedekind domains. Hints of dimension theory.Core Documentation
M. F. Atiyah, I. G. Macdonald, Introduction to Commutative Algebra. Addison-Wesley, 1996.M. Reid, Undergraduate Algebraic Geometry, Cambridge University Press, 1988.
D. Eisenbud, Commutative Algebra with a view toward Algebraic Geometry, Springer-Verlag, 1995.
A. Gathmann, Commutative Algebra, Lecture notes.
Type of delivery of the course
Frontal lectures, suggested exercises.Type of evaluation
The exam is written and oral. There will be two midterms (that may exempt from the written exam)