Definition:Trivial Annihilator

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Let $\struct {R, +, \times}$ be a ring or, more usually, a field.

From Annihilator of Ring Always Contains Zero, we have that $0 \in \map {\mathrm {Ann} } R$ whatever the ring $R$ is.

$R$ is said to have a trivial annihilator if and only if its annihilator $\map {\mathrm {Ann} } R$ consists only of the integer $0$.

Also see