Solitons: Differential equations, symmetries, and infinite-dimensional algebras
《Solitons: Differential equations, symmetries, and infinite-dimensional algebras》 · 第 571–572 页 · Definition/Proposition B.76
A local noetherian ring $(A,\mathfrak m)$ with residue field $k$ is called regular if the following equivalent conditions are satisfied: (i) $\dim A=\dim_k\mathfrak m/\mathfrak m^2$. (ii) $\operatorname{gr}_{\mathfrak m}(A)\cong k[T_1,\ldots,T_d]$. (iii) $\mathfrak m$ can be generated by $\dim A$ elements.