When cyclic singular modules over a simple ring are injective

Authors: Đinh Văn Huỳnh, Jain Surender Kumar, Sergio Lopez-Permouth,

https://doi.org/10.1016/S0021-8693(03)00065-6

Publisher, magazine: ,

Publication year: 2003

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Abstract

Let \(R\) be a simple ring. It is shown that \(R\) is Morita equivalent to a right PCI (proper cyclics are injective) domain if and only if every singular cyclic right \(R\)-module is quasi-continuous, and furthermore if every proper cyclic right \(R\)-module is quasi-continuous then the right uniform dimension of \(R\) is at most 2.

Tags: right PCI domains; simple rings; Morita equivalences; singular cyclic right modules; quasi-continuous modules; right uniform dimension