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<p>In this paper, we deal with the ring of Hurwitz series, denoted by <i>HR</i>, where <i>R</i> is a ring. We begin by providing a complete characterization of its <i>z</i>-ideals. Moreover, we investigate the minimal prime ideals of Hurwitz series rings, presenting various conditions which ensure that <i>HP</i> is a minimal prime ideal for each minimal prime ideal <i>P</i> of <i>R</i>. Based on these results, we study the <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(z^{\circ }\)</EquationSource> </InlineEquation>-ideals of <i>HR</i>. Several examples are presented to illustrate and delimit our results.</p>

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z-ideals, z°-ideals, and minimal prime ideals in Hurwitz series rings

  • 期刊论文

  • 发表日期：

    2025年10月15日

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  • Ahmed Maatallah

摘要

In this paper, we deal with the ring of Hurwitz series, denoted by HR, where R is a ring. We begin by providing a complete characterization of its z-ideals. Moreover, we investigate the minimal prime ideals of Hurwitz series rings, presenting various conditions which ensure that HP is a minimal prime ideal for each minimal prime ideal P of R. Based on these results, we study the \(z^{\circ }\) -ideals of HR. Several examples are presented to illustrate and delimit our results.