A regular local ring is a Noetherian commutative unital local ring whose Krull dimension agrees with the minimal number of generators of its maximal ideal . Equivalently, the Krull dimension equals where is the residue field of . A Noetherian local ring is regular iff its global dimension is finite; it follows that its global and Krull dimension coincide.
The notion should not be confused with that of a von Neumann regular ring? in noncommutative algebra.
Last revised on June 26, 2023 at 16:09:45. See the history of this page for a list of all contributions to it.