Seminormal ring

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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 Swan (1980) as a simplification of the original definition of Traverso (1970).

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 nodel 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.

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