The term annihilator is used in several different ways in various aspects of mathematics. It is most commonly used to mean the set of all functions satisfying given conditions and vanishing on every member of a given set.
For a module 
over a commutative ring 
, its annihilator is the ideal
 |
For an inclusion of commutative rings 
, the annihilator of the 
-module 
is the conductor ideal
(Stacks Project Authors 2026).
