Then two " m "-primary ideals I \ subset J have the same integral closure if and only if they have the same multiplicity.
12.
He was an invited speaker at the International Congress of Mathematicians in 1990 in Kyoto ( " Absolute Integral Closure and Big Cohen-Macaulay Algebras " ).
13.
The normalization of a projective variety is projective; in fact, it's the Proj of the integral closure of some homogeneous coordinate ring of " X ".
14.
*PM : integral closures in separable extensions are finitely generated, id = 9323 new !-- WP guess : integral closures in separable extensions are finitely generated-- Status:
15.
*PM : integral closures in separable extensions are finitely generated, id = 9323 new !-- WP guess : integral closures in separable extensions are finitely generated-- Status:
16.
In general, the integral closure of a noetherian domain of dimension at most 2 is noetherian; Nagata gave an example of dimension 3 noetherian domain whose integral closure is not noetherian.
17.
In general, the integral closure of a noetherian domain of dimension at most 2 is noetherian; Nagata gave an example of dimension 3 noetherian domain whose integral closure is not noetherian.
18.
In 1954, in a joint paper with Northcott, Rees introduced the " Northcott-Rees theory of reductions and integral closures " which has subsequently been influential in commutative algebra.
19.
A commutative ring R contained in a ring S is said to be "'integrally closed "'in S if R is equal to the integral closure of R in S.
20.
On the other hand, the interaction between the integral closure and completion has been among the most important aspects that distinguish modern commutative ring theory from the classical one developed by the likes of Noether.
