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<p>This paper introduces the concept of (2,&#xa0;<i>r</i>)-ideals in commutative rings. This notion has been initiated given a generalizing understanding beyond 2-nil ideals. Some examples with properties showing clear interrelations of (2,&#xa0;<i>r</i>)-ideals with other well-defined ideal types, including the 2-absorbing ideals and <i>n</i>-ideals, are investigated and seen through this scope. The main contribution of this paper is the characterization of a ring where every (2,&#xa0;<i>r</i>)-ideal is also a prime ideal and to find a complete description of (2,&#xa0;<i>r</i>)-ideals of such a ring. This work pushes forward the ideal theory’s theoretical framework with a new understanding of structural aspects in commutative algebra.</p>

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On (2, r)-ideals of commutative rings

  • 期刊论文

  • 发表日期：

    2025年5月29日

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  • Izzat Qaralleh,
  • Abdelhaq El Khalfi

摘要

This paper introduces the concept of (2, r)-ideals in commutative rings. This notion has been initiated given a generalizing understanding beyond 2-nil ideals. Some examples with properties showing clear interrelations of (2, r)-ideals with other well-defined ideal types, including the 2-absorbing ideals and n-ideals, are investigated and seen through this scope. The main contribution of this paper is the characterization of a ring where every (2, r)-ideal is also a prime ideal and to find a complete description of (2, r)-ideals of such a ring. This work pushes forward the ideal theory’s theoretical framework with a new understanding of structural aspects in commutative algebra.