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<p>We explore the existence of <i>n</i>-submodules in the context of module theory. Then we generalize our results by considering an additive, left-exact functor <i>F</i> defined on the category of modules, which is either covariant or contravariant, and preserves multiplications. Within this broader framework, we identify and characterize an <i>n</i>-submodule of <i>F</i>(<i>M</i>), derived from the structure of <i>M</i> and the action of the functor <i>F</i>.</p>

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n-submodules of modules over commutative rings

  • 期刊论文

  • 发表日期：

    2025年11月19日

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  • Somayeh Karimzadeh

摘要

We explore the existence of n-submodules in the context of module theory. Then we generalize our results by considering an additive, left-exact functor F defined on the category of modules, which is either covariant or contravariant, and preserves multiplications. Within this broader framework, we identify and characterize an n-submodule of F(M), derived from the structure of M and the action of the functor F.