The coheight of a proper ideal 
of a commutative Noetherian unit ring 
is the Krull dimension
of the quotient ring 
.
The coheight is related to the height of 
by the inequality
(Bruns and Herzog 1998, p. 367). Equality holds for particular classes of rings, e.g., for local Cohen-Macaulay rings (Bruns
and Herzog 1998, p. 58).
See also
Codimension,
Height,
Krull Dimension
This entry contributed by Margherita
Barile
Explore with Wolfram|Alpha
References
Bruns, W. and Herzog, J. Cohen-Macaulay Rings, 2nd ed. Cambridge, England: Cambridge University Press, 1998.Kunz,
E. Introduction
to Commutative Algebra and Algebraic Geometry. Boston, MA: Birkhäuser,
p. 40, 1985.Referenced on Wolfram|Alpha
Coheight
Cite this as:
Barile, Margherita. "Coheight." From MathWorld--A Wolfram Web Resource, created by Eric
W. Weisstein. https://mathworld.wolfram.com/Coheight.html
Subject classifications
