Geodesic
On weakened $(\alpha ,\delta )$-skew Armendariz rings
Mathematica Bohemica, Tome 147 (2022) no. 2, pp. 187-200
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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 $n$.
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 $n$.
DOI : 10.21136/MB.2021.0005-20
Classification : 16S36, 16S50, 16S99
Keywords: Armendariz ring; $(\alpha, \delta )$-skew Armendariz ring; weak Armendariz ring; weak $(\alpha, \delta )$-skew Armendariz ring 
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Farahani, Alireza Majdabadi; Maghasedi, Mohammad; Heydari, Farideh; Tavallaee, Hamidagha. On weakened $(\alpha ,\delta )$-skew Armendariz rings. Mathematica Bohemica, Tome 147 (2022) no. 2, pp. 187-200. doi: 10.21136/MB.2021.0005-20

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