Abstract
In this paper we study the transfer of an algebraic property, namely the right weak Beachy-Blair condition, that was introduced in Salem et al. (Rendiconti del Circolo Matematico di Palermo Series 2. https://doi.org/10.1007/s12215-016-0262-x, 2017), between a base ring R and two classes of extensions over R, namely skew monoid rings and Ore extension rings.