Dualizing module

In algebra, a dualizing module, also called a canonical module, is a module over a commutative ring that is analogous to the canonical bundle of a smooth variety and that appears in several duality theorems.

Definition

A dualizing module for a Noetherian ring R is a finitely-generated module M such that for any maximal ideal m, the R/m vector space Extⁿ
_R(R/m,M) vanishes if n≠ height(m) and is 1-dimensional if n=height(m).}}