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<p>We consider a module <i>G</i> over a right nearring <i>N</i>. We define the large ideal graph of <i>G</i>. For a finitely generated <i>N</i>-group, we prove that its large ideal graph has diameter at most 3 and provide an equivalent condition for <i>G</i> to be completely reducible. We prove several properties which involve connectedness, diameter and completeness etc. of graphs obtained from large ideals and strictly large ideals of <i>G</i>. Significant examples are given to illustrate various notions.</p>

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Graph with respect to large ideals of an N-group

  • 期刊论文

  • 发表日期：

    2025年7月8日

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  • Rajani Salvankar,
  • H. L. Yashaswini,
  • Kedukodi Babushri Srinivas,
  • Harikrishnan Panackal,
  • Kuncham Syam Prasad

摘要

We consider a module G over a right nearring N. We define the large ideal graph of G. For a finitely generated N-group, we prove that its large ideal graph has diameter at most 3 and provide an equivalent condition for G to be completely reducible. We prove several properties which involve connectedness, diameter and completeness etc. of graphs obtained from large ideals and strictly large ideals of G. Significant examples are given to illustrate various notions.