ON RINGS OVER WHICH THE INJECTIVE HULL OF EACH CYCLIC MODULE IS Σ-EXTENDING
2012 ◽
Vol 12
(01)
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pp. 1250127
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Carl Faith (2003) introduced and investigated an interesting class of rings over which every cyclic right module has Σ-injective injective hull (abbr., right CSI-rings). Inspired by this we investigate rings over which every cyclic right R-module has a Σ-extending injective hull. We call such rings right CSE-rings and show that the class of right CSE-rings and that of right CSI-rings coincide. We also use other hulls of cyclic modules to define other classes of rings, and investigate their structure. We prove, among others, that a ring R is right QI if and only if the quasi-injective hull of each cyclic right module is Σ-injective.
2020 ◽
Vol 21
(4)
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pp. 429-438
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2007 ◽
Vol 73
(18)
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pp. 5832-5839
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1968 ◽
Vol 11
(1)
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pp. 19-21
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2018 ◽
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