Definition:Annihilator on Algebraic Dual

Definition
Let $R$ be a commutative ring.

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 $M$, denoted $M^\circ$, is 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