Ideals and Factor Rings of Centrally Essential Rings

2022/04/22 by Lyubimtsev, Oleg, Tuganbaev, Askar
#FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2204.10507

Abstract

It is proved that the ring R with center Z(R), such that the module R_Z(R) is an essential extension of the module Z(R)_Z(R), is not necessarily right quasi-invariant, i.e., maximal right ideals of the ring R are not necessarily ideals. We use central essentiality to obtain conditions which are sufficient to the property that all maximal right ideals are ideals

Related

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• Rings which are Essential over their Centers, II
• Distributive Invariant Centrally Essential Rings
• Completely Centrally Essential Rings
• Rings Which Are Essential over Their Centers