| $2$-Primal环的Ore扩张中的极小素理想和单位元 |
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| 引用本文： | 王英瑛,陈卫星.$2$-Primal环的Ore扩张中的极小素理想和单位元[J].数学研究及应用,2018,38(4):378-383. |
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| 作者姓名： | 王英瑛 陈卫星 |
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| 作者单位： | 山东工商学院数学与信息科学学院, 山东 烟台 264005,山东工商学院数学与信息科学学院, 山东 烟台 264005 |
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| 摘 要： | Let R be an(α,δ)-compatible ring.It is proved that R is a 2-primal ring if and only if for every minimal prime ideal P in Rx;α,δ] there exists a minimal prime ideal P in R such that P = P x;α,δ],and that f(x) ∈ Rx;α,δ] is a unit if and only if its constant term is a unit and other coefficients are nilpotent.
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| 收稿时间： | 2017/7/10 0:00:00 |
| 修稿时间： | 2018/4/27 0:00:00 |
Minimal Prime Ideals and Units in 2-Primal Ore Extensions |
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| Yingying WANG and Weixing CHEN.Minimal Prime Ideals and Units in 2-Primal Ore Extensions[J].Journal of Mathematical Research with Applications,2018,38(4):378-383. |
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| Authors: | Yingying WANG and Weixing CHEN |
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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 $Rx;\alpha,\delta]$ there exists a minimal prime ideal $P$ in $R$ such that $\mathscr{P}=Px;\alpha,\delta]$, and that $f(x)\in Rx;\alpha,\delta]$ is a unit if and only if its constant term is a unit and other coefficients are nilpotent. |
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| Keywords: | $2$-primal ring $(\alpha \delta)$-compatible ring Ore extension |
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