  We search for principal ideals. As a sample, let $R$ be a strongly-normal,
almost-factorial, and complete-intersection local ring with a prime ideal $P$
of height one. If $depth(R/ P)\geq dim R-2$, we show $P$ is principal. As an
immediate corollary, we apply some easy local cohomology arguments and reprove
a celebrated theorem of Auslander-Buchsbaum, simplifying a result of Dao and
Samuel. From this, we show the hypersurface property of rings of multiplicity
at most three. As another application, we answer affirmatively a question
posted by Braun.
