Communications of the
Korean Mathematical Society CKMS

A commutative ring $R$ with unityis called EM-Hermite if for each $a,b\in R$ there exist $c,d,f\in R$ such that $a=cd,b=cf$ and the ideal $(d,f)$ is regular in $R$. We showed in this article that $R$ is a PP-ring if and only if the idealization $R(+)R$ is an EM-Hermite ring if and only if $R[x]/(x^{n+1})$ is an EM-Hermite ring for each $n\in \mathbb{N}$. We generalize some results, and answer some questions in the literature.

Keywords: EM-Hermite ring, PP-ring, idealization

MSC numbers: 13A, 13B25, 13B30, 13C10