Abstract
In this work we introduce virtual versions of H-supplemented modules and NS-modules. These modules are defined by replacing the condition of being a “direct summand” with being “isomorphic to a direct summand”. The paper explores various equivalent conditions for a module to be virtually H-supplemented and investigates their fundamental properties. It is discovered that over a right V-ring for a module, the concepts virtually H-supplemented, virtually semisimple and VNS, coincide. Additionally, it is proven that each right R-module is VNS if and only if every noncosingular right R-module is injective.
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Asgari, S., Talebi, Y. & Hamzekolaee, A.R.M. Exploring virtual versions of H-supplemented and NS-modules. Beitr Algebra Geom (2023). https://doi.org/10.1007/s13366-023-00719-6
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DOI: https://doi.org/10.1007/s13366-023-00719-6
Keywords
- Small submodule
- Direct summand
- H-supplemented module
- Virtually H-supplemented module
- NS-module
- Virtually NS-module