Then the formal power series ring AX is completely integrally closed.
2.
Note sometimes in combinatorial literature the difference between normal and integrally closed is blurred.
3.
Integrally closed domains also play a role in the hypothesis of the Going-down theorem.
4.
Indeed, the integral closure is contained in the intersection since the valuation rings are integrally closed.
5.
It is a standard algebra exercise to show this implies that " R " is an integrally closed domain.
6.
An integral domain is completely integrally closed if and only if the monoid of divisors of " A " is a group.
7.
The normality property is invariant under affine-lattice isomorphisms of lattice polytopes and the integrally closed property is invariant under an affine change of coordinates.
8.
*PM : examples of integrally closed extensions, id = 9311 new !-- WP guess : examples of integrally closed extensions-- Status:
9.
*PM : examples of integrally closed extensions, id = 9311 new !-- WP guess : examples of integrally closed extensions-- Status:
10.
This implies in particular that an integral element over an integrally closed domain " A " has a minimal polynomial over " A ".
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