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http://dx.doi.org/10.4134/CKMS.c210167

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)
Publication Information
Communications of the Korean Mathematical Society / v.37, no.2, 2022 , pp. 399-407 More about this Journal
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.
Keywords
von Neumann regular ring; strongly regular ring; GP-injective essential maximal ideal;
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