Quasi-duo and weakly duo skew pbw extensions

In this paper we study the quasi-duo and weakly duo properties for skew PBW extensions. We show that if A is a right quasi-duo skew PBW extension over a ring R, then R is right quasi-duo, and that for a right quasi-duo graded skew PBW extension A over R, the zero-degree homogeneous component of R is left quasi-duo if and only if A is left quasi-duo. Moreover, we give a characterization of right quasi-duo rings for a particular kind of bijective quasi-commutative skew PBW extensions. We also show some properties of weakly left or right duo skew PBW extensions.