ADS modules

We study the class of ADS rings and modules introduced by Fuchs (1970) [F]. We give some connections between this notion and classical notions such as injectivity and quasi-continuity. A simple ring R such that R R is ADS must be either right self-injective or indecomposable as a right R-module. Und...

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Veröffentlicht in:	Journal of algebra 2012-02, Vol.352 (1), p.215-222
Hauptverfasser:	Alahmadi, Adel, Jain, S.K., Leroy, André
Format:	Artikel
Sprache:	eng
Schlagworte:	ADS modules Direct sums Injective modules Mathematics Modules Quasi-continuous modules Rings and Algebras
Online-Zugang:	Volltext
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Beschreibung
Zusammenfassung:	We study the class of ADS rings and modules introduced by Fuchs (1970) [F]. We give some connections between this notion and classical notions such as injectivity and quasi-continuity. A simple ring R such that R R is ADS must be either right self-injective or indecomposable as a right R-module. Under certain conditions we can construct a unique ADS hull up to isomorphism. We introduce the concept of completely ADS modules and characterize completely ADS semiperfect right modules as direct sum of semisimple and local modules.
ISSN:	0021-8693 1090-266X
DOI:	10.1016/j.jalgebra.2011.10.035