Essential ideal of a matrix nearring and ideal related properties of graphs-Reference-Cited by-同舟云学术

Essential ideal of a matrix nearring and ideal related properties of graphs

Published:2024-05-31 Issue: Volume:42 Page:1-12
ISSN:2175-1188
Container-title:Boletim da Sociedade Paranaense de Matemática
language:
Short-container-title:B Soc Paran Mat

Author:

Salvankar Rajani^ORCID,Babushri Srinivas Kedukodi^ORCID,Panackal Harikrishnan^ORCID,Prasad Kuncham Syam^ORCID

Abstract

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 $\mathcal{L}_{g}(H)$) defined on generalized essential ideals of a finitely generated module $H$ over $N$. We prove a characterization for $\mathcal{L}_{g}(H)$ to be complete. We also prove $\mathcal{L}_{g}(H)$ has diameter at-most 2 and obtain related properties with suitable illustrations.

Publisher

Sociedade Paranaense de Matemática

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