Source: wikibot/auslander-buchsbaum-formula
= Auslander–Buchsbaum formula
{wiki=Auslander–Buchsbaum_formula}
The Auslander–Buchsbaum formula is a significant result in commutative algebra and homological algebra that relates the projective dimension of a module to its depth and the dimension of the ring over which the module is defined. Specifically, it provides a way to compute the projective dimension of a finitely generated module over a Noetherian ring.