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. A local ring has dimension 0 if and only if its maximal ideal is nilpotent.
Read more about Krull Dimension: Explanation, Krull Dimension and Schemes, Examples, Krull Dimension of A Module
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