On rings whose essential maximal right ideals are GP-injective}
Commun. Korean Math. Soc.
Published online December 6, 2021
Jeonghee Jeong and 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
MSC numbers : 16E50; 16D50
Full-Text :

   

Copyright © Korean Mathematical Society.
The Korea Science Technology Center (Rm. 411), 22, Teheran-ro 7-gil, Gangnam-gu, Seoul 06130, Korea
Tel: 82-2-565-0361  | Fax: 82-2-565-0364  | E-mail: paper@kms.or.kr   | Powered by INFOrang Co., Ltd