Permeable Rings and Their Extensions

Let us call a ring R to be right permeable if for any α ∈ R; Rα = 0, then αR = 0. Left permeable and permeable rings are defined analogously. These rings are generalized reversible rings with a privileging role that permeability inherited in its several extensions where reversibility seized to be inherited. It will be proved that full matrix ring, polynomial ring, Laurent polynomial ring, Dorroh extension, group ring and Ore extensions of a right (left) permeable ring are right (left) permeable rings. Moreover, the same holds for Barnett matrix rings with their extensions in different quotient polynomials and matrix forms.