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 
.
Gorenstein Ring
See also
Cayley-Bacharach Theorem, Cohen-Macaulay RingExplore with Wolfram|Alpha
References
Eisenbud, D.; Green, M.; and Harris, J. "Cayley-Bacharach Theorems and Conjectures." Bull. Amer. Math. Soc. 33, 295-324, 1996.Referenced on Wolfram|Alpha
Gorenstein RingCite this as:
Weisstein, Eric W. "Gorenstein Ring." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/GorensteinRing.html