  For ungraded quotients of an arbitrary $\mathbb{Z}$-graded ring, we define
the general PBW property, that covers the classical PBW property and the
$N$-type PBW property studied via the $N$-Koszulity by several authors ([BG1],
BG2], [FV]). In view of the noncommutative Gr\"obner basis theory, we conclude
that every ungraded quotient of a path algebra (or a free algebra) has the
general PBW property. We remark that an earlier result of Golod [Gol]
concerning Gr\"obner bases can be used to give a homological characterization
of the general PBW property in terms of Shafarevich complex. Examples of
application are given.
