J. Korean Math. Soc. 2014; 51(4): 721-734
Printed July 1, 2014
https://doi.org/10.4134/JKMS.2014.51.4.721
Copyright © The Korean Mathematical Society.
Fatemeh Esmaeili Khalil Saraei
University of Tehran
Let $M$ be a module over a commutative ring $R$, and let $T(M)$ be its set of torsion elements. The total torsion element graph of $M$ over $R$ is the graph $T(\Gamma(M))$ with vertices all elements of $M$, and two distinct vertices $m$ and $n$ are adjacent if and only if $m+n\in T(M)$. In this paper, we study the basic properties and possible structures of two (induced) subgraphs $Tor_{0}(\Gamma(M))$ and $T_{0}(\Gamma(M))$ of $T(\Gamma(M))$, with vertices $T(M)\setminus \{0\}$ and $M\setminus \{0\}$, respectively. The main purpose of this paper is to extend the definitions and some results given in \cite{6} to a more general total torsion element graph case.
Keywords: total graph, torsion prime submodule, $T$-reduced
MSC numbers: Primary 05C99, 13C13
2012; 49(1): 85-98
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