Idealization of EM-Hermite rings
Commun. Korean Math. Soc. 2020 Vol. 35, No. 1, 13-20
Published online January 31, 2020
Hiba Abdelkarim, Emad Abuosba, Manal Ghanem
Mathematics Department; Mathematics Department; Mathematics Department
Abstract : 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
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