2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/116405For 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 Gröbner 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 Gröbner bases can be used to give a homological characterization of the general PBW property in terms of Shafarevich complex. Examples of application are given.15 pages, Algebra Colloquium, in pressRepresentation TheoryRings and Algebras16W70; 16Z05text