https://mathworld.wolfram.com/KrullDimension.html

If is a ring (commutative with 1), the height of a prime ideal is defined as the supremum of all so that there is a chain where all are distinct prime ideals. Then, the Krull dimension of is defined as the supremum of all the heights of all its prime ideals.
Krull Dimension
See alsoPrime Ideal
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ReferencesEisenbud, D. Commutative Algebra with a View Toward Algebraic Geometry. New York: Springer-Verlag, 1995.Atiyah, M. F. and Macdonald, I. G. Introduction to Commutative Algebra. Reading, MA: Addison-Wesley, 1969.
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Cite this as:
Weisstein, Eric W. "Krull Dimension." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/KrullDimension.html