Mathematica Bohemica, Vol. 147, No. 2, pp. 187-200, 2022
On weakened $(\alpha,\delta)$-skew Armendariz rings
Alireza Majdabadi Farahani, Mohammad Maghasedi, Farideh Heydari, Hamidagha Tavallaee
Received January 12, 2020. Published online May 20, 2021.
Abstract: In this note, for a ring endomorphism $\alpha$ and an $\alpha$-derivation $\delta$ of a ring $R$, the notion of weakened $(\alpha,\delta)$-skew Armendariz rings is introduced as a generalization of $\alpha$-rigid rings and weak Armendariz rings. It is proved that $R$ is a weakened $(\alpha,\delta)$-skew Armendariz ring if and only if $T_n(R)$ is weakened $(\bar{\alpha},\bar{\delta})$-skew Armendariz if and only if $R[x]/(x^n)$ is weakened $(\bar{\alpha},\bar{\delta})$-skew Armendariz ring for any positive integer $n$.
