Applications of powerful theorems in Bruns -Herzog's book "Cohen-Macaulay Rings" It seems that theorem 1.4.13 and it's corollary of Bruns and Herzog's book Cohen-Macaulay Rings, are powerful tools but I don't see any example that shows the power of it. My original question was an example that shows the power of it in use, but I change it as you see below to be more useful for me and others:   

What is your favorite powerful theorem in commutative algebra, especially in the book Cohen-Macaulay Rings by Bruns and Herzog? 

Please give an example that shows the power of it in use, with a hint that shows the application of that theorem  in that example. 

Auslander--Buchsbaum formula.
  example: as "11156" says "everybody who read commutative algebra knows examples", but for example:
Matt E's solution for my question: (R is a regular local ring of dimension $d$, and $I$ an ideal. If $R/I$ has depth $d − 1$, then $I$ is principal.)
