Regular Local Ring

A regular local ring is a Local Ring $R$ with Maximal Ideal $m$ so that $m$ can be generated with exactly $d$ elements where $d$ is the Krull Dimension of the Ring $R$. Equivalently, R is regular if the Vector Space $m/m^2$ has dimension $d$.

See also Krull Dimension, Local Ring, Regular Ring, Ring

References

Eisenbud, D. Commutative Algebra with a View Toward Algebraic Geometry. New York: Springer-Verlag, p. 242, 1995.