See also
Codimension,
Coheight,
Ideal,
Krull Dimension,
Prime Ideal,
Proper Ideal
This entry contributed by Margherita
Barile
Explore with Wolfram|Alpha
References
Atiyah, M. F. and Macdonald, I. G. Introduction to Commutative Algebra. Reading, MA: Addison-Wesley 1969.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,
1985.Matsumura, H. Commutative
Ring Theory. Cambridge, England: Cambridge University Press, 1986.Nagata,
M. Local
Rings. Huntington, NY: Krieger, 1975.Samuel, P. and Zariski,
O. Commutative
Algebra I. Princeton, NJ: Van Nostrand, 1958.Sharp, R. Y.
Steps
in Commutative Algebra, 2nd ed. Cambridge, England: Cambridge University
Press, 2000.Referenced on Wolfram|Alpha
Ideal Height
Cite this as:
Barile, Margherita. "Ideal Height." From MathWorld--A Wolfram Web Resource, created by Eric
W. Weisstein. https://mathworld.wolfram.com/IdealHeight.html
Subject classifications
.
The height of a proper prime
ideal 
of 
is the maximum of the lengths 
of the chains of prime ideals
contained in 
,
is the minimum of the heights of the prime
ideals containing 
.
