Minimal Prime Ideals and Units in 2-Primal Ore Extensions

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.