Commutative algebra 59: Krull's principal ideal theorem скачать в хорошем качестве

Commutative algebra 59: Krull's principal ideal theorem

This lecture is part of an online course on commutative algebra, following the book "Commutative algebra with a view toward algebraic geometry" by David Eisenbud. We give some applications of the theorems we proved about the dimension of local rings. We first show that the dimension of a local ring is the same as that of its completion. Then we give some variations of the principal that "the zeros of a function should have codimension 1". In particular we prove Krull's principal ideal theorem, which says roughly that that ll irreducible components of the zeros of a function have codimension 1 provided the function is not a zero divisor. Reading: Section Exercises: