On rings whose essential maximal right ideals are GP-injective
Commun. Korean Math. Soc. 2022 Vol. 37, No. 2, 399-407
https://doi.org/10.4134/CKMS.c210167
Published online March 29, 2022
Printed April 30, 2022
Jeonghee Jeong, Nam Kyun Kim
Hanbat National University; Hanbat National University
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 $\pi$-regular.
Keywords : von Neumann regular ring, strongly regular ring, GP-injective essential maximal ideal
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