On weakened $(\alpha,\delta)$-skew Armendariz rings
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 $(\alpha,\delta)$-...
Main Authors: | , , , |
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Format: | Article |
Language: | English |
Published: |
Institute of Mathematics of the Czech Academy of Science
2022-07-01
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Series: | Mathematica Bohemica |
Subjects: | |
Online Access: | http://mb.math.cas.cz/full/147/2/mb147_2_4.pdf |
Summary: | 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 $n$. |
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ISSN: | 0862-7959 2464-7136 |