Generalized PP and Zip Subrings of Matrix Rings

Abstract

Let $R$ be an abelian ring. We consider a special subring $A_n$, relative to $α_2, · · · , α_n ∈ R{\rm End}(R)$, of the matrix ring $M_n(R)$ over a ring $R$. It is shown that the ring $A_n$ is a generalized right PP-ring (right zip ring) if and only if the ring $R$ is a generalized right PP-ring (right zip ring). Our results yield more examples of generalized right PP-rings and right zip rings.