In this paper, we consider matrix maps over a zero-symmetric right nearring N with 1. We define the notions of essential ideal, superfluous ideal, generalized essential ideal of a matrix nearring and prove results which exhibit the interplay between these ideals and the corresponding ideals of the base nearring N. We discuss the combinatorial properties such as connectivity, diameter, completeness of a graph (denoted by Lg(H)) defined on generalized essential ideals of a finitely generated module H over N. We prove a characterization for Lg(H) to be complete. We also prove Lg(H) has diameter at-most 2 and obtain related properties with suitable illustrations.
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Salvankar et al. (2024) studied this question.
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