A regular local ring is a local ring 
with maximal ideal 
so that 
can be generated with exactly 
elements where 
is the Krull dimension
of the ring 
. Equivalently, R is regular if the vector
space 
has dimension 
.
Regular Local Ring
See also
Krull Dimension, Local Ring, Localization, Regular Ring, RingExplore with Wolfram|Alpha
References
Eisenbud, D. Commutative Algebra with a View Toward Algebraic Geometry. New York: Springer-Verlag, p. 242, 1995.Referenced on Wolfram|Alpha
Regular Local RingCite this as:
Weisstein, Eric W. "Regular Local Ring." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/RegularLocalRing.html