Maybe it is too easy but I want to know that: If $R$ is regular local ring of Krull dimension $2$ and $m$ is the maximal ideal of $R$. (It means that height $m$ is $2$). Can we find any ideal of height $2$ different from $m$?
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closed as offtopic by Todd Trimble♦ Jul 23 at 13:03This question appears to be offtopic. The users who voted to close gave this specific reason:



No. Since it is the unique maximal ideal, $\mathfrak m$ contains every prime ideal (its complement is the set of all units of $R$). 

