In algebra, a seminormal ring is a commutative reduced ring in which, whenever x, y satisfy , there is s with and . 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 , or the ring of a nodal curve. In general, a reduced scheme can be said to be seminormal if every morphism 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. References Charles Weibel, The K-book: An introduction to algebraic K-theory Commutative algebra Ring theory