Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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IDEALIZATION OF EM-HERMITE RINGS

  • Abdelkarim, Hiba (The University of Jordan School of Science Mathematics Department) ;
  • Abuosba, Emad (The University of Jordan School of Science Mathematics Department) ;
  • Ghanem, Manal (The University of Jordan School of Science Mathematics Department)
  • Received : 2018.11.17
  • Accepted : 2019.03.13
  • Published : 2020.01.31
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Abstract

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.

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References

  1. E. Abuosba and M. Ghanem, Annihilating content in polynomial and power series rings, To appear in J. Korean Math. Soc.
  2. S. Endo, Note on p.p. rings. (A supplement to Hattori's paper), Nagoya Math. J. 17 (1960), 167-170. http://projecteuclid.org/euclid.nmj/1118800460 https://doi.org/10.1017/S0027763000002129
  3. M. Ghanem and E. Abu Osba, Some extensions of generalized morphic rings and EM-rings, An. Stiint. Univ. "Ovidius" Constanta Ser. Mat. 26 (2018), no. 1, 111-123. https://doi.org/10.2478/auom-2018-0007
  4. M. Ghanem and E. Abu Osba, EM-Hermite rings, Submitted.
  5. T.-K. Lee and Y. Zhou, Morphic rings and unit regular rings, J. Pure Appl. Algebra 210 (2007), no. 2, 501-510. https://doi.org/10.1016/j.jpaa.2006.10.005
  6. T.-K. Lee and Y. Zhou, Regularity and morphic property of rings, J. Algebra 322 (2009), no. 4, 1072-1085. https://doi.org/10.1016/j.jalgebra.2009.04.046
  7. H. Zhu and N. Ding, Generalized morphic rings and their applications, Comm. Algebra 35 (2007), no. 9, 2820-2837. https://doi.org/10.1080/00927870701354017