Let "\\{I_n\\}_{n\\in\\mathbb N}" be ideals of "\\{0\\}", such that "I_n\\subset I_{n+1}" ("I_n\\supset I_{n+1}") for every "n". Since "I_n=I_{n+1}=\\{0\\}" for every "n\\ge 1", we obtain that "\\{0\\}" is a noetherian (an artinian) ring.
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