Minimal Prime Ideals and Units in 2-Primal Ore Extensions |
Received:July 10, 2017 Revised:April 27, 2018 |
Key Words:
$2$-primal ring $(\alpha,\delta)$-compatible ring Ore extension
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Fund Project:Supported by the Natural Foundation of Shandong Province in China (Grant No.ZR2013AL013). |
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Abstract: |
Let $R$ be an $(\alpha,\delta)$-compatible ring. It is proved that $R$ is a 2-primal ring if and only if for every minimal prime ideal $\mathscr{P}$ in $R[x;\alpha,\delta]$ there exists a minimal prime ideal $P$ in $R$ such that $\mathscr{P}=P[x;\alpha,\delta]$, and that $f(x)\in R[x;\alpha,\delta]$ is a unit if and only if its constant term is a unit and other coefficients are nilpotent. |
Citation: |
DOI:10.3770/j.issn:2095-2651.2018.04.005 |
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