• Communications of the Korean Mathematical Society
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• v.35 no.1
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• pp.13-20
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• 2020

A commutative ring R with unityis called EM-Hermite if for each a, b ∈ R there exist c, d, f ∈ 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]/(xⁿ⁺¹) is an EM-Hermite ring for each n ∈ ℕ. We generalize some results, and answer some questions in the literature.