Graph with respect to large ideals of an N-group

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

doi:10.1007/s13226-025-00823-4

Graph with respect to large ideals of an N-group

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

^*Corresponding author for this work

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

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.

Original language	English
Pages (from-to)	1078-1089
Number of pages	12
Journal	Indian Journal of Pure and Applied Mathematics
Volume	56
Issue number	3
DOIs	https://doi.org/10.1007/s13226-025-00823-4
Publication status	Published - 09-2025

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

Access to Document

10.1007/s13226-025-00823-4

Cite this

@article{0280ad45536646f5a1824a1f562aa17d,

title = "Graph with respect to large ideals of an N-group",

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.",

author = "Rajani Salvankar and Yashaswini, \{H. L.\} and Srinivas, \{Kedukodi Babushri\} and Harikrishnan Panackal and Prasad, \{Kuncham Syam\}",

note = "Publisher Copyright: {\textcopyright} The Indian National Science Academy 2025.",

year = "2025",

month = sep,

doi = "10.1007/s13226-025-00823-4",

language = "English",

volume = "56",

pages = "1078--1089",

journal = "Indian Journal of Pure and Applied Mathematics",

issn = "0019-5588",

publisher = "Indian National Science Academy",

number = "3",

}

TY - JOUR

T1 - Graph with respect to large ideals of an N-group

AU - Salvankar, Rajani

AU - Yashaswini, H. L.

AU - Srinivas, Kedukodi Babushri

AU - Panackal, Harikrishnan

AU - Prasad, Kuncham Syam

N1 - Publisher Copyright: © The Indian National Science Academy 2025.

PY - 2025/9

Y1 - 2025/9

N2 - 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.

AB - 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.

UR - https://www.scopus.com/pages/publications/105010031836

UR - https://www.scopus.com/pages/publications/105010031836#tab=citedBy

U2 - 10.1007/s13226-025-00823-4

DO - 10.1007/s13226-025-00823-4

M3 - Article

AN - SCOPUS:105010031836

SN - 0019-5588

VL - 56

SP - 1078

EP - 1089

JO - Indian Journal of Pure and Applied Mathematics

JF - Indian Journal of Pure and Applied Mathematics

IS - 3

ER -

Graph with respect to large ideals of an N-group

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this