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. It is used in Grothendieck local duality.

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).}}

References

• Bourbaki, N. (2007), Algèbre commutative. Chapitre 10, Éléments de mathématique (in French), Springer-Verlag, Berlin, ISBN 978-3-540-34394-3; 3-540-34394-6, MR2333539 {{citation}}: Check |isbn= value: invalid character (help)
• Bruns, Winfried; Herzog, Jürgen (1993), Cohen-Macaulay rings, Cambridge Studies in Advanced Mathematics, vol. 39, Cambridge University Press, ISBN 978-0-521-41068-7, MR1251956