ANN-essentially injective modules

Fadel, Zahraa Abbas; Nayef, Mahdi Saleh

doi:10.47974/JDMSC-2719

Open Access Research Article

ANN-essentially injective modules

^*Zahraa Abbas FadelCorresponding authorzhmaster93@uomustansiriyah.edu.iqDepartment of Mathematics College of Education Mustansiriyah UniversityBaghdad, IraqView full profile → , Mahdi Saleh Nayefmahdisaleh773@uomustansiriyah.edu.iqDepartment of Mathematics College of Education Mustansiriyah UniversityDepartment of Mathematics College of Education Mustansiriyah UniversityBaghdad, IraqView full profile →

* Corresponding author · click or hover a name for details

pp. 2161–2167Vol. 29Issue 5May 2026DOI: 10.47974/JDMSC-2719 Crossmark XML

Received:: 01 Jan 2026
Published Online:: 22 May 2026
Article type:: Research Article
Language:: EN
Article no.:: JDMSC-2719
Pages:: 2161–2167

Abstract

This paper investigates the concept of annihilator essential injectivity in the setting of R-modules, where R is unital ring. An R-module M2 is termed annihilator essentially M1-injective if every R-homomorphism from A ≤ M1 to M2 with an annihilator essential kernel can be extended to M1. We prove that this injective property is closed under taking submodules and factor modules of M1, as well as direct products. By providing illustrative examples, we demonstrate the distinction between annihilator essential injectivity and other classical forms of injectivity. These findings provide new insights into the study of relative injectivity and the classification of modules.

Keywords

Injective modules Essentially injective modules Annihilator essentially injective modules Annihilator essential submodule Essential submodule

Subject Classifications

Primary 16D10Secondary 16D50

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