Coheight
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)<=dimR |
(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 DimensionThis entry contributed by Margherita Barile
Explore with Wolfram|Alpha
WolframAlpha
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
CoheightCite this as:
Barile, Margherita. "Coheight." From MathWorld--A Wolfram Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/Coheight.html