Volume 26, Issue 3
Generalized PP and Zip Subrings of Matrix Rings

Commun. Math. Res., 26 (2010), pp. 193-202.

Published online: 2021-05

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• 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.

• Keywords

generalized right PP-ring, PP-ring, right zip ring.

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@Article{CMR-26-193, author = {Zhongkui and Liu and and 18244 and and Zhongkui Liu and Husheng and Qiao and and 18245 and and Husheng Qiao}, title = {Generalized PP and Zip Subrings of Matrix Rings}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {26}, number = {3}, pages = {193--202}, 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.

}, issn = {2707-8523}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cmr/19149.html} }
TY - JOUR T1 - Generalized PP and Zip Subrings of Matrix Rings AU - Liu , Zhongkui AU - Qiao , Husheng JO - Communications in Mathematical Research VL - 3 SP - 193 EP - 202 PY - 2021 DA - 2021/05 SN - 26 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cmr/19149.html KW - generalized right PP-ring, PP-ring, right zip ring. AB -

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.

ZhongkuiLiu & HushengQiao. (2021). Generalized PP and Zip Subrings of Matrix Rings. Communications in Mathematical Research . 26 (3). 193-202. doi:
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