Integrally closed domain

Summary

An integrally closed domain, or normal domain, is an integral domain that contains every element of its field of fractions that is integral over it. Every unique factorisation domain is integrally closed, and so is every Dedekind domain and every valuation ring. The going-down theorem holds over integrally closed domains. In geometry, integrally closed domains are the coordinate rings of normal varieties, whose singular points form a set of codimension at least two.