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For a commutative ring $R$ with $1$, I am looking for an equivalent condition for an ideal $T$ to have the property that $T$ has a unique maximal sub ideal in $R$, equivalently, the sum of proper sub ideal of $T$ is not equal to $T$.

For a commutative ring $R$ with unity, I am looking for an equivalent condition for an ideal $T$ to have the property that $T$ contains a unique maximal proper subideal, equivalently, the sum of proper subideals of $T$ is not equal to $T$.