Idealization of EM-Hermite rings
Commun. Korean Math. Soc.
Published online July 2, 2019
Hiba Abdelkarim, Emad Abuosba, and Manal Ghanem
The University of Jordan
Abstract : A commutative ring with unity R is 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 generalise 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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