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 .
See also Krull Dimension, Local Ring, Regular Ring, Ring
Eisenbud, D. Commutative Algebra with a View Toward Algebraic Geometry. New York:
Springer-Verlag, p. 242, 1995.