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    A commutative ring is a field if and only if its only ideals are $0$ and $R$

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    A nonzero commutative ring is a field exactly when it has no nontrivial ideals.Suggest a slogan

    Let \(R\) be a commutative ring with \(1\). Then \(R\) is a field if and only if the set of ideals of \(R\) is exactly \(\theset{0, R}\) with \(0 \neq R\).

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