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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.
}, issn = {2707-8523}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cmr/19149.html} }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.