Superfluous ideals of module over nearrings
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Keywords:
$N$-group, Nearring, Superfluous ideal graphAbstract
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 $\mathcal{S}_{G}$. 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.
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