Geodesic
Rings characterized by cyclic modules
Glasgow mathematical journal, Tome 31 (1989) no. 2, pp. 251-256

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A ring R is called right PCI if every proper cyclic right R-module is injective, i.e. if C is a cyclic right R-module then CR ≅ RR or CR is injective. By [2] and [3], if R is a non-artinian right PCI ring then R is a right hereditary right noetherian simple domain. Such a domain is called a right PCI domain. The existence of right PCI domains is guaranteed by an example given in [2]. As generalizations of right PCI rings, several classes of rings have been introduced and investigated, for example right CDPI rings, right CPOI rings (see [8], [6]). In Section 2 we define right PCS, right CPOS and right CPS rings and study the relationship between all these rings. 
Huynh, Dinh van; Dan, Phan. Rings characterized by cyclic modules. Glasgow mathematical journal, Tome 31 (1989) no. 2, pp. 251-256. doi: 10.1017/S0017089500007801
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