A generalization of the extending property for semimodules via weakly supplement subsemimodules

Dawood, Shimaa M.; Al-Saadi, Saad A.

doi:10.47974/JDMSC-2702

Open Access Research Article

A generalization of the extending property for semimodules via weakly supplement subsemimodules

^*Shimaa M. DawoodCorresponding authorShamaa_84@uomustansiriyah.edu.iqDepartment of MathematicsCollege of ScienceMustansiriyah UniversityBaghdad, Iraq0000-0003-4238-6565View full profile → , Saad A. Al-Saadisaalsaadi@uomustansiriyah.edu.iqDepartment of MathematicsCollege of ScienceMustansiriyah UniversityBaghdad, Iraq0000-0002-6369-8173View full profile →

* Corresponding author · click or hover a name for details

pp. 2421–2430Vol. 29Issue 6June 2026DOI: 10.47974/JDMSC-2702 Crossmark XML

Received:: 01 Nov 2025
Published Online:: 13 Jun 2026
Article type:: Research Article
Language:: EN
Article no.:: JDMSC-2702
Pages:: 2421–2430

Abstract

This work introduces and investigates a generalization of extending semimodules via weak-supplement subsemimodules. An S-semimodule L is called weakly-supplement extending (shortly, 𝓌𝓈e—semimodule) if every subsemimodule of L is essential in a weakly-supplement subsemimodule of L. We asserted that the class of 𝓌𝓈e-semimodules properly contains both extending and lifting semimodules. Analogously to extending semimodules, this paper gives many characterizations of 𝓌𝓈e-semimodules. We showed that L is wse-semimodule if and only if each closed subsemimodule of L is a weakly supplement subsemimodule of L. Moreover, we discussed the relation of wse-semimodule and its relation with other known classes of semimodule, such as ⨁-supplemented, lifting, and uniform semimodules. We inspected whether the 𝓌𝓈e-semimodule property is satisfied under direct sum, subsemimodule, epimorphic image, and inverse image.

Keywords

Semiring Extending semimodule Weakly-supplement subsemimodule Lifting semimodule

Subject Classifications

16Y6016Y80

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