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Volume 32, Issue 3
On Skew Triangular Matrix Rings

Weiliang Wang, Yao Wang & Yanli Ren

DOI: 10.13447/j.1674-5647.2016.03.08

Commun. Math. Res., 32 (2016), pp. 259-271.

Published online: 2021-05

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  • Abstract

Let $α$ be a nonzero endomorphism of a ring $R$, $n$ be a positive integer and $T_n(R, α)$ be the skew triangular matrix ring. We show that some properties related to nilpotent elements of $R$ are inherited by $T_n(R, α)$. Meanwhile, we determine the strongly prime radical, generalized prime radical and Behrens radical of the ring $R[x; α]/(x^n)$, where $R[x; α]$ is the skew polynomial ring.

  • Keywords

skew triangular matrix ring, skew polynomial ring, weak zip property, strongly prime radical, generalized prime radical.

  • AMS Subject Headings

16N20, 16S36

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CMR-32-259, author = {Wang , WeiliangWang , Yao and Ren , Yanli}, title = {On Skew Triangular Matrix Rings}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {32}, number = {3}, pages = {259--271}, abstract = {

Let $α$ be a nonzero endomorphism of a ring $R$, $n$ be a positive integer and $T_n(R, α)$ be the skew triangular matrix ring. We show that some properties related to nilpotent elements of $R$ are inherited by $T_n(R, α)$. Meanwhile, we determine the strongly prime radical, generalized prime radical and Behrens radical of the ring $R[x; α]/(x^n)$, where $R[x; α]$ is the skew polynomial ring.

}, issn = {2707-8523}, doi = {https://doi.org/10.13447/j.1674-5647.2016.03.08}, url = {http://global-sci.org/intro/article_detail/cmr/18897.html} }
TY - JOUR T1 - On Skew Triangular Matrix Rings AU - Wang , Weiliang AU - Wang , Yao AU - Ren , Yanli JO - Communications in Mathematical Research VL - 3 SP - 259 EP - 271 PY - 2021 DA - 2021/05 SN - 32 DO - http://doi.org/10.13447/j.1674-5647.2016.03.08 UR - https://global-sci.org/intro/article_detail/cmr/18897.html KW - skew triangular matrix ring, skew polynomial ring, weak zip property, strongly prime radical, generalized prime radical. AB -

Let $α$ be a nonzero endomorphism of a ring $R$, $n$ be a positive integer and $T_n(R, α)$ be the skew triangular matrix ring. We show that some properties related to nilpotent elements of $R$ are inherited by $T_n(R, α)$. Meanwhile, we determine the strongly prime radical, generalized prime radical and Behrens radical of the ring $R[x; α]/(x^n)$, where $R[x; α]$ is the skew polynomial ring.

Wang , WeiliangWang , Yao and Ren , Yanli. (2021). On Skew Triangular Matrix Rings. Communications in Mathematical Research . 32 (3). 259-271. doi:10.13447/j.1674-5647.2016.03.08
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