Commutative Algebra with a View Toward Algebraic Geometry
《Commutative Algebra with a View Toward Algebraic Geometry》 · 第 462 页 · Section 21.6「Complete Intersections」
We say that a ring $R$ is a complete intersection if there is a regular ring $S$ and a regular sequence $x_1,\ldots,x_n\in S$ such that $R\cong S/(x_1,\ldots,x_n)$. $R$ is locally a complete intersection if this is true for $R_P$ for every maximal ideal $P$ of $R$.