TY - JOUR
T1 - Superfluous ideals in module over nearrings
AU - Salvankar, Rajani
AU - Prasad, Kuncham Syam
AU - Srinivas, Kedukodi Babushri
AU - Panackal, Harikrishnan
N1 - Publisher Copyright:
© 2023, Erdal Karapinar. All rights reserved.
PY - 2023/9/17
Y1 - 2023/9/17
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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U2 - 10.31838/rna/2023.06.03.003
DO - 10.31838/rna/2023.06.03.003
M3 - Article
AN - SCOPUS:85175039927
SN - 2636-7556
VL - 6
SP - 66
EP - 75
JO - Results in Nonlinear Analysis
JF - Results in Nonlinear Analysis
IS - 3
ER -