Maybe it is so easy but i want to know that: If R is regular local rings 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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No. Since it is the unique maximal ideal, $\mathfrak m$ contains every prime ideal (its complement is the set of all units of $R$). |
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