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