Superfluous ideals in module over nearrings

Rajani Salvankar; Kuncham Syam Prasad; Kedukodi Babushri Srinivas; Harikrishnan Panackal

doi:10.31838/rna/2023.06.03.003

Superfluous ideals in module over nearrings

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

^*Corresponding author for this work

Manipal Institute of Technology, Manipal

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

Nearrings are non-linear algebraic systems. Zero-divisor graphs based on algebraic structures like rings, module over rings are well-known. In this paper, we consider the module over a right nearring, (say, G). We define the superfluous ideal graph of G, denoted as G. We obtain that if G has DCCI, then S_G has diameter at most 3. We characterize the set of ideals of G with degree 1 in S_G when G is completely reducible. Furthermore, we prove several properties of superfluous ideal graphs which involve connectivity, completeness, etc. with explicit examples of these notions.

Original language	English
Pages (from-to)	66-75
Number of pages	10
Journal	Results in Nonlinear Analysis
Volume	6
Issue number	3
DOIs	https://doi.org/10.31838/rna/2023.06.03.003
Publication status	Published - 17-09-2023

All Science Journal Classification (ASJC) codes

Analysis
Mathematics (miscellaneous)
Geometry and Topology
Applied Mathematics

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10.31838/rna/2023.06.03.003

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AU - Panackal, Harikrishnan

PY - 2023/9/17

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N2 - Nearrings are non-linear algebraic systems. Zero-divisor graphs based on algebraic structures like rings, module over rings are well-known. In this paper, we consider the module over a right nearring, (say, G). We define the superfluous ideal graph of G, denoted as G. We obtain that if G has DCCI, then SG has diameter at most 3. We characterize the set of ideals of G with degree 1 in SG when G is completely reducible. Furthermore, we prove several properties of superfluous ideal graphs which involve connectivity, completeness, etc. with explicit examples of these notions.

AB - Nearrings are non-linear algebraic systems. Zero-divisor graphs based on algebraic structures like rings, module over rings are well-known. In this paper, we consider the module over a right nearring, (say, G). We define the superfluous ideal graph of G, denoted as G. We obtain that if G has DCCI, then SG has diameter at most 3. We characterize the set of ideals of G with degree 1 in SG when G is completely reducible. Furthermore, we prove several properties of superfluous ideal graphs which involve connectivity, completeness, etc. with explicit examples of these notions.

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Superfluous ideals in module over nearrings

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