The Krull dimension of a commutative ring 
with multiplicative
identity is the supremum of the heights of its prime ideals. The height of a prime
ideal 
is the supremum of all nonnegative
integers 
for which there is a chain 
of distinct prime
ideals.
Krull Dimension
See also
Module Depth, 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