** Annie Krull, operatic soprano ( died 1947 )

** Krull ( video game ), the arcade, Atari and pinball adaptations of that film

** Krull topology

** Krull – Akizuki theorem

** Craig Krull Gallery, Santa Monica, CA, The Last Days of Pompeii, September 7-October 12.

** Craig Krull Gallery, Los Angeles, CA, 100 Boots Revisited.

** the image of the boundary of the closed ball is contained in the union of a finite number of elements of the partition, each having cell dimension less than n.

** Lebesgue covering dimension, a definition of dimension using topological properties

** Minkowski – Bouligand dimension

** Spaces with integer dimension are better-behaved than spaces with fractal dimension.

** Hypersphere, a round sphere of dimension higher than 2, especially if embedded in such a space

** the unit sphere ( with superscript denoting dimension )

** Complex dimension

** Hausdorff dimension

** Inductive dimension

** Lebesgue covering dimension

** Packing dimension

** Isoperimetric dimension

Commutative rings in which prime ideals are maximal are known as zero-dimensional rings, where the dimension used is the Krull dimension.

In commutative algebra, the Krull dimension of a ring R, named after Wolfgang Krull ( 1899 – 1971 ), is the supremum of the number of strict inclusions in a chain of prime ideals.

The Krull dimension need not be finite even for a Noetherian ring.

A field k has Krull dimension 0 ; more generally, has Krull dimension n. A principal ideal domain that is not a field has Krull dimension 1.

We define the Krull dimension of to be the supremum of the heights of all of its primes.

Nagata gave an example of a ring that has infinite Krull dimension even though every prime ideal has finite height.

It follows readily from the definition of the spectrum of a ring, the space of prime ideals of equipped with the Zariski topology, that the Krull dimension of is precisely equal to the irreducible dimension of its spectrum.

* An integral domain is a field if and only if its Krull dimension is zero.

In general, a Noetherian ring is Artinian if and only if its Krull dimension is 0.

If R is a commutative ring, and M is an R-module, we define the Krull dimension of M to be the Krull dimension of the quotient of R making M a faithful module.

This property suggests a deep theory of dimension for Noetherian rings beginning with the notion of the Krull dimension.