Volume 32, Issue 3
On Skew Triangular Matrix Rings

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.

16N20, 16S36

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@Article{CMR-32-259, author = {Weiliang and Wang and and 18552 and and Weiliang Wang and Yao and Wang and and 18553 and and Yao Wang and Yanli and Ren and and 18463 and and Yanli Ren}, 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.

Weiliang Wang, Yao Wang & Yanli Ren. (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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