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.

**References**

Eisenbud, D. *Commutative Algebra with a View Toward Algebraic Geometry.* New York: Springer-Verlag, 1995.

Macdonald, I. G. and Atiyah, M. F. *Introduction to Commutative Algebra.* Reading, MA: Addison-Wesley, 1969.

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1999-05-26