(untitled) (Communications in Mathematical Research, 2021)
Let R be an abelian ring. We consider a special subring A_n, relative to α_2, · · · , α_n ∈ REnd(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.