Annihilator
- Pure Mathematics -
Algebra Dictionary
Definition
Given a ring R and an R-module M, the annihilator of a subset S ⊆ M is the ideal Ann_R(S) = { r in R | r·s = 0 for all s in S }; for a single element m it is Ann_R(m). For the whole module M one gets the annihilator ideal Ann_R(M).