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<p>Let <i>R</i> be a commutative ring with identity and <i>M</i> a unitary <i>R</i>-module. The purpose of this paper is to introduce the concept of semi-<i>n</i>-submodules as an extension of semi <i>n</i>-ideals and <i>n</i>-submodules. A proper submodule <i>N</i> of <i>M</i> is called a semi <i>n</i>-submodule if whenever <i>r</i> ∈ <i>R</i>, <i>m</i> ∈ <i>M</i> with <i>r</i><sup>2</sup><i>m</i> ∈ <i>N</i>, <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(r\notin\sqrt{0}\)</EquationSource> <EquationSource Format="MATHML"><math display="block"> <mi>r</mi> <mo>∉</mo> <msqrt> <mn>0</mn> </msqrt> </math></EquationSource> </InlineEquation> and Ann<sub><i>R</i></sub>(<i>m</i>) = 0, then <i>rm</i> ∈ <i>N</i>. Several properties, characterizations of this class of submodules with many supporting examples are presented. Furthermore, semi <i>n</i>-submodules of amalgamated modules are investigated.</p>

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Semi n-submodules of modules over commutative rings

  • 期刊论文

  • 发表日期：

    2026年1月26日

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  • Hani A. Khashan,
  • Ece Yetkin Çelikel

摘要

Let R be a commutative ring with identity and M a unitary R-module. The purpose of this paper is to introduce the concept of semi-n-submodules as an extension of semi n-ideals and n-submodules. A proper submodule N of M is called a semi n-submodule if whenever r ∈ R, m ∈ M with r2m ∈ N, \(r\notin\sqrt{0}\) r ∉ 0 and AnnR(m) = 0, then rm ∈ N. Several properties, characterizations of this class of submodules with many supporting examples are presented. Furthermore, semi n-submodules of amalgamated modules are investigated.