A regular local ring is a Noetherian local ring 
whose maximal ideal 
can be generated by 
elements, where 
is the Krull dimension
of 
.
Equivalently, 
has vector space dimension 
over the residue
field 
.
Regular Local Ring
See also
Big Cohen-Macaulay Module, Gersten Conjecture, Krull Dimension, Local Ring, Localization, Regular Ring, Ring, Serre's Intersection Multiplicity, System of ParametersExplore 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 Resource. https://mathworld.wolfram.com/RegularLocalRing.html