A Noetherian local ring is regular when the minimal number of generators of its maximal ideal equals its Krull dimension. Every regular local ring is an integral domain and a unique factorization domain.
Articles by others on the same topic
A **regular local ring** is a specific type of local ring that has a well-behaved structure in relation to its maximal ideal and its associated residue field. To define it more precisely: 1. **Local Ring**: A local ring \( R \) is a commutative ring with a unique maximal ideal \( \mathfrak{m} \).