Definition:Annihilator on Algebraic Dual

Definition
Let $R$ be a commutative ring with unity.

Let $G$ be a module over $R$.

Let $G^*$ be the algebraic dual of $G$.

Let $M$ be a submodule of $G$.

The annihilator of $M$ is denoted and defined as:


 * $M^\circ := \set {t \in G^*: \forall x \in M: \map t x = 0}$

Also denoted as
Some sources denote this as $\map {\operatorname {Ann} } M$.

Also see

 * Definition:Annihilator