In algebra, a seminormal ring is a commutative reduced ring in which, whenever x, y satisfy
A basic example is an integrally closed domain, i.e., a normal ring.
For an example which is not normal, one can consider the non-integral ring
, or the ring of a nodal curve.
In general, a reduced scheme
which induces a homeomorphism of topological spaces, and an isomorphism on all residue fields, is an isomorphism of schemes.
This commutative algebra-related article is a stub.