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<p>In this article, we define a module <i>H</i> to be fully invariant ECS-module if and only if for each fully invariant ec-closed submodule of <i>H</i> is a direct summand. We investigate fully invariant ECS-modules and locate this property among the other generalizations of the CS notion. This new class of modules is a proper generalization of each of fully invariant extending and ECS-modules. It is well known that the class of ECS-modules is not closed under direct sums, while in this paper, we show that fully invariant ECS-modules are closed under direct sums.</p>

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Modules whose fully invariant ec-closed submodules are direct summands

  • 期刊论文

  • 发表日期：

    2025年8月9日

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  • Enas Mustafa Kamil,
  • Haneen Siraj Ibrahim

摘要

In this article, we define a module H to be fully invariant ECS-module if and only if for each fully invariant ec-closed submodule of H is a direct summand. We investigate fully invariant ECS-modules and locate this property among the other generalizations of the CS notion. This new class of modules is a proper generalization of each of fully invariant extending and ECS-modules. It is well known that the class of ECS-modules is not closed under direct sums, while in this paper, we show that fully invariant ECS-modules are closed under direct sums.