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<p>Let <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(F=R^{(n)}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>F</mi> <mo>=</mo> <msup> <mi>R</mi> <mrow> <mo stretchy="false">(</mo> <mi>n</mi> <mo stretchy="false">)</mo> </mrow> </msup> </mrow> </math></EquationSource> </InlineEquation> be a free <i>R</i>-module of finite rank <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(n\ge 2\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>n</mi> <mo>≥</mo> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation> and <i>S</i> be a multiplicatively closed subset of <i>R</i>. In this paper, we characterize the <i>S</i>-prime submodules of <i>F</i> with at most <i>n</i> generators, when <i>R</i> is a <i>UFD</i> or a Dedekind domain. Also, we define the concept of the <i>S</i>-primary decomposition and give an <i>S</i>-primary decomposition for some submodules <i>N</i> of <i>M</i>.</p>

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A Characterization of S-Prime and S-Primary Decomposition of Submodules of a Module Over a Dedekind Domain

  • 期刊论文

  • 发表日期：

    2025年8月31日

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  • F. Mirzaei,
  • R. Nekooei

摘要

Let \(F=R^{(n)}\) F = R ( n ) be a free R-module of finite rank \(n\ge 2\) n ≥ 2 and S be a multiplicatively closed subset of R. In this paper, we characterize the S-prime submodules of F with at most n generators, when R is a UFD or a Dedekind domain. Also, we define the concept of the S-primary decomposition and give an S-primary decomposition for some submodules N of M.