Minimal Prime Ideals and Units in 2-Primal Ore Extensions
Received:July 10, 2017  Revised:April 27, 2018
Key Word: $2$-primal ring   $(\alpha,\delta)$-compatible ring   Ore extension  
Fund ProjectL:Supported by the Natural Foundation of Shandong Province in China (Grant No.ZR2013AL013).
Author NameAffiliation
Yingying WANG School of Mathematics and Information Science, Shandong Institute of Business and Technology, Shandong 264005, P. R. China 
Weixing CHEN School of Mathematics and Information Science, Shandong Institute of Business and Technology, Shandong 264005, P. R. China 
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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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