# Kommutativer Ring/Ideal/Superhöhe/en/Definition

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Let ${\displaystyle {}R}$ be a noetherian commutative ring and let ${\displaystyle {}I\subseteq R}$ be an ideal. The (noetherian) superheight is the supremum

${\displaystyle \operatorname {sup} _{}^{}{\left(\operatorname {ht} _{}^{}{\left(IS\right)}:\,S{\text{ is a notherian }}R-{\text{algebra}}\right)}.}$