Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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ON RINGS WHOSE ESSENTIAL MAXIMAL RIGHT IDEALS ARE GP-INJECTIVE

  • Jeong, Jeonghee (Department of Mathematical Sciences Hanbat National University) ;
  • Kim, Nam Kyun (Department of Mathematical Sciences Hanbat National University)
  • Received : 2021.05.07
  • Accepted : 2021.07.07
  • Published : 2022.04.30
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Abstract

In this paper, we continue to study the von Neumann regularity of rings whose essential maximal right ideals are GP-injective. It is proved that the following statements are equivalent: (1) R is strongly regular; (2) R is a 2-primal ring whose essential maximal right ideals are GP-injective; (3) R is a right (or left) quasi-duo ring whose essential maximal right ideals are GP-injective. Moreover, it is shown that R is strongly regular if and only if R is a strongly right (or left) bounded ring whose essential maximal right ideals are GP-injective. Finally, we prove that a PI-ring whose essential maximal right ideals are GP-injective is strongly π-regular.

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Acknowledgement

We sincerely thank the referee for comments which improved the paper. This paper contains some results from Master's thesis of the first author.

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