Mori domain

In algebra, a Mori domain, named after Yoshiro Mori by Querré (1971, 1976), is an integral domain satisfying the ascending chain condition on integral divisorial ideals.

A commutative ring is a Krull domain if and only if it is a Mori domain and completely integrally closed.

[1] A polynomial ring over a Mori domain need not be a Mori domain.

Also, the complete integral closure of a Mori domain need not be a Mori (or, equivalently, Krull) domain.

This commutative algebra-related article is a stub.