Commun. Math. Res., 32 (2016), pp. 259-271.
Published online: 2021-05
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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} }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.