Abstract: It is well-known that, using principal weak flatness
property, some important monoids are characterized, such as regular
monoids, left almost regular monoids, and so on. In this article, we
define a generalization of principal weak flatness called GP-Flatness,
and will characterize monoids by this property of their right (Rees
factor) acts. Also we investigate new classes of monoids called
generally regular monoids and generally left almost regular monoids.