Let $R$ be Noetherian ring and $f \in R \backslash R^*$. According to Krull's principal ideal theorem we get for the Krull dimension $dim(R / fR) \le dim(R) -1$.
Why do we have an equality $dim(R / fR) = dim(R) -1$ if $f$ is a regular element?
2026-03-28 02:49:00.1774666140
$dim(R / fR) = dim(R) -1$ if $f$ Regular
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