ADS modules

Adel Alahmadi (1) , S.K. Jain (2) , André Leroy (3)

1 department of Mathematics
2 Department of Mathematics, Ohio University, Athens
3 LML - Laboratoire de Mathématiques de Lens

We study the class of ADS rings and modules introduced by Fuchs. We give some connections between this notion and classical notions such as injectivity and quasi-continuity. A simple ring R such that R is ADS as a right R-module 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.

Mots clés: Injective; relative injective; CS modules

Domaines: Anneaux et algèbres [math.RA]

Adel Alahmadi, S.K. Jain, André Leroy. ADS modules. Journal of Algebra, 2012, 352 (1), pp.215-222. ⟨hal-00715411⟩