Commutative Algebra with a View Toward Algebraic Geometry
《Commutative Algebra with a View Toward Algebraic Geometry》 · 第 470 页 · Chapter 19「Homological Theory of Regular Local Rings」
We define the projective dimension of $M$, written $\operatorname{pd}M$, to be the minimum of the lengths of projective resolutions of $M$; it is $\infty$ if $M$ has no finite projective resolution.