Seminormal ring

In algebra, a seminormal ring is a commutative reduced ring in which, whenever "x", "y" satisfy formula_1, there is "s" with formula_2 and formula_3. This definition was given by as a simplification of the original definition of . 
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 formula_4, or the ring of a nodal curve.
In general, a reduced scheme formula_5 can be said to be seminormal if every morphism formula_6 which induces a homeomorphism of topological spaces, and an isomorphism on all residue fields, is an isomorphism of schemes.
A semigroup is said to be seminormal if its semigroup algebra is seminormal.