When learning algebraic geometry and in particular the notion of smooth varieties, you will probably stumble upon the following Theorems:

• Regular local rings are factorial.
• Localizations of regular local rings are regular, too.
• A local ring is regular iff its residue field has finite projective dimension (Serre).

Many texts on algebraic geometry take this as a black box, quoting standard sources of commutative algebra. The reason seems to be that you don't have to understand the methods of the proof (e.g. Koszul homology) in order to apply these results.