Nicholson, W. K.; Park, J. K.; Yousif, M. F. Principally quasi-injective modules. (English) Zbl 0924.16004 Commun. Algebra 27, No. 4, 1683-1693 (1999). The paper deals with properties and characterizations of principally quasi-injective \(R\)-modules, i.e., modules for which each \(R\)-homomorphism from a principal submodule of \(M\) to \(M\) can be extended to an endomorphism of \(M\). This is a generalization of both quasi-injective modules and principally injective modules. Many of the properties of these two classes of modules are extended to principally quasi-injective modules. Properties covered include those relating to the Jacobson radical, the endomorphism ring and uniform submodules. Reviewer: F.Théron (Pretoria) Cited in 2 ReviewsCited in 15 Documents MSC: 16D50 Injective modules, self-injective associative rings Keywords:principally quasi-injective modules; endomorphism rings; Jacobson radicals; uniform submodules; principally injective modules PDF BibTeX XML Cite \textit{W. K. Nicholson} et al., Commun. Algebra 27, No. 4, 1683--1693 (1999; Zbl 0924.16004) Full Text: DOI References: [1] Camillo V., Portugaliae Math 46 pp 33– (1989) [2] DOI: 10.1007/BF02761306 · Zbl 0802.16010 [3] DOI: 10.1080/00927878908823714 · Zbl 0659.16016 [4] DOI: 10.1080/00927879608825785 · Zbl 0858.16002 [5] DOI: 10.4153/CJM-1976-109-2 · Zbl 0317.16005 [6] DOI: 10.1006/jabr.1995.1117 · Zbl 0839.16004 [7] DOI: 10.1112/plms/s3-28.2.291 · Zbl 0294.16003 [8] DOI: 10.1080/00927878608823297 · Zbl 0592.13008 [9] Wisbauer R., Foundations of Module and Ring Theory (1991) · Zbl 0746.16001 [10] DOI: 10.1090/S0002-9947-1972-0286843-3 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.