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October 2020 Perpendicular graph of modules
Maryam SHIRALI, Ehsan MOMTAHAN, Saeed SAFAEEYAN
Hokkaido Math. J. 49(3): 463-479 (October 2020). DOI: 10.14492/hokmj/1607936538

Abstract

Let $R$ be a ring and $M$ be an $R$-module. Two modules $A$ and $B$ are called orthogonal, written $A\perp B$, if they do not have non-zero isomorphic submodules. We associate a graph $\Gamma_{\bot}(M)$ to $M$ with vertices $\mathcal{M}_{\perp}=\{(0)\neq A\leq M \mid \exists B\neq (0) \;\mbox{such that}\; A\perp B\}$, and for distinct $A,B\in \mathcal{M}_{\perp}$, the vertices $A$ and $B$ are adjacent if and only if $A\perp B$. The main object of this article is to study the interplay of module-theoretic properties of $M$ with graph-theoretic properties of $\Gamma_{\bot}(M)$. An algorithm is given to generate perpendicular graphs of $\mathbb{Z}_n$.

Citation

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Maryam SHIRALI. Ehsan MOMTAHAN. Saeed SAFAEEYAN. "Perpendicular graph of modules." Hokkaido Math. J. 49 (3) 463 - 479, October 2020. https://doi.org/10.14492/hokmj/1607936538

Information

Published: October 2020
First available in Project Euclid: 14 December 2020

Digital Object Identifier: 10.14492/hokmj/1607936538

Subjects:
Primary: 05C25
Secondary: 16D10

Rights: Copyright © 2020 Hokkaido University, Department of Mathematics

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Vol.49 • No. 3 • October 2020
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