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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.
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참고문헌 (7)
참고문헌 신청
Emad Abu Osba / 2019 / Annihilating content in polynomial and power series rings / 대한수학회지 56(5):1403~1418
S. Endo / 1960 / Note on p.p. rings. (A supplement to Hattori's paper) / Nagoya Math. J. 17:167~170
M. Ghanem / 2018 / Some extensions of generalized morphic rings and EM-rings / An. Stiint. Univ. "Ovidius" Constanta Ser. Mat. 26(1):111~123
M. Ghanem / EM-Hermite rings
T. -K. Lee / 2007 / Morphic rings and unit regular rings / J. Pure Appl. Algebra 210(2):501~510
S. Endo / 1960 / Note on p.p. rings. (A supplement to Hattori's paper) / Nagoya Math. J. 17:167~170
M. Ghanem / 2018 / Some extensions of generalized morphic rings and EM-rings / An. Stiint. Univ. "Ovidius" Constanta Ser. Mat. 26(1):111~123
M. Ghanem / EM-Hermite rings
T. -K. Lee / 2007 / Morphic rings and unit regular rings / J. Pure Appl. Algebra 210(2):501~510
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