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Rings characterized by cyclic modules

Published online by Cambridge University Press:  18 May 2009

Dinh van Huynh
Institute of Mathematics, P.O. Box 631 Bo Hô, Hanoi, Vietnam
Phan Dan
Institute of Mathematics, P.O. Box 631 Bo Hô, Hanoi, Vietnam
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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 CRRR 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.

Research Article
Copyright © Glasgow Mathematical Journal Trust 1989


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