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  and , 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 . As generalizations of right PCI rings, several classes of rings have been introduced and investigated, for example right CDPI rings, right CPOI rings (see , ). In Section 2 we define right PCS, right CPOS and right CPS rings and study the relationship between all these rings.
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