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 also
Prime IdealExplore with Wolfram|Alpha
References
Atiyah, M. F. and Macdonald, I. G. Introduction to Commutative Algebra. Reading, MA: Addison-Wesley, 1969.Eisenbud, D. Commutative Algebra with a View Toward Algebraic Geometry. New York: Springer-Verlag, 1995.Referenced on Wolfram|Alpha
Krull DimensionCite this as:
Weisstein, Eric W. "Krull Dimension." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/KrullDimension.html