The coheight of a proper ideal I of a commutative Noetherian unit ring R is the Krull dimension of the quotient ring R/I. The coheight is related to the height of I by the inequality height(I) + coheight(I)<=dim R (Bruns and Herzog 1998, p. 367). Equality holds for particular classes of rings, e.g., for local Cohen-Macaulay rings.

codimension | height | Krull dimension