Seminormal ring explained
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 .
, or the ring of a nodal curve.
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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