Gorenstein Ring

An algebraic Ring which appears in treatments of duality in Algebraic Geometry. Let $A$ be a local Artinian Ring with $m\subset A$ its maximal Ideal. Then $A$ is a Gorenstein ring if the Annihilator of $m$ has Dimension 1 as a Vector Space over $K=A/m$.

See also Cayley-Bacharach Theorem

References

Eisenbud, D.; Green, M.; and Harris, J. ``Cayley-Bacharach Theorems and Conjectures.'' Bull. Amer. Math. Soc. 33, 295-324, 1996.