Graph with respect to large ideals of an N-group

Rajani Salvankar (), H. L. Yashaswini (), Kedukodi Babushri Srinivas (), Harikrishnan Panackal () and Kuncham Syam Prasad ()
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Rajani Salvankar: Mangalore Institute Technology & Engineering (Visvesvaraya Technological University, Belagavi)
H. L. Yashaswini: Manipal Institute of Technology
Kedukodi Babushri Srinivas: Manipal Institute of Technology
Harikrishnan Panackal: Manipal Institute of Technology
Kuncham Syam Prasad: Manipal Institute of Technology

Indian Journal of Pure and Applied Mathematics, 2025, vol. 56, issue 3, 1078-1089

Abstract: Abstract 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.

Keywords: N-group; Nearring; Essential ideal graph (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s13226-025-00823-4

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