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<p>Let <i>G</i> be an abelian group and <i>R</i> be a <i>G</i>-graded integral domain. Recall that an integral domain is a Goldman domain if the intersection of all nonzero prime ideals is a nonzero ideal. The main aim of this paper is to introduce the concept of a graded Goldman domain, which is a graded integral domain in which the intersection of all nonzero graded prime ideals is nonzero. We give some characterizations of graded Goldman domains and we show that <i>R</i> is a graded Goldman domain if and only if there exists a graded maximal ideal <i>M</i> of <i>R</i>[<i>X</i>] such that <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(R\cap M=0.\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>R</mi> <mo>∩</mo> <mi>M</mi> <mo>=</mo> <mn>0</mn> <mo>.</mo> </mrow> </math></EquationSource> </InlineEquation></p>

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On the graded Goldman domain

  • 期刊论文

  • 发表日期：

    2026年6月30日

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  • Yassir Mata,
  • Mohamed Aqalmoun

摘要

Let G be an abelian group and R be a G-graded integral domain. Recall that an integral domain is a Goldman domain if the intersection of all nonzero prime ideals is a nonzero ideal. The main aim of this paper is to introduce the concept of a graded Goldman domain, which is a graded integral domain in which the intersection of all nonzero graded prime ideals is nonzero. We give some characterizations of graded Goldman domains and we show that R is a graded Goldman domain if and only if there exists a graded maximal ideal M of R[X] such that \(R\cap M=0.\) R ∩ M = 0 .