THE TOTAL TORSION ELEMENT GRAPH WITHOUT THE ZERO ELEMENT OF MODULES OVER COMMUTATIVE RINGS

Title & Authors
THE TOTAL TORSION ELEMENT GRAPH WITHOUT THE ZERO ELEMENT OF MODULES OVER COMMUTATIVE RINGS
Saraei, Fatemeh Esmaeili Khalil;

Abstract
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 $\small{T({\Gamma}(M))}$ with vertices all elements of M, and two distinct vertices m and n are adjacent if and only if $\small{m+n{\in}T(M)}$. In this paper, we study the basic properties and possible structures of two (induced) subgraphs $\small{Tor_0({\Gamma}(M))}$ and $\small{T_0({\Gamma}(M))}$ of $\small{T({\Gamma}(M))}$, with vertices $\small{T(M){\backslash}\{0\}}$ and $\small{M{\backslash}\{0\}}$, respectively. The main purpose of this paper is to extend the definitions and some results given in [6] to a more general total torsion element graph case.
Keywords
total graph;torsion prime submodule;T-reduced;
Language
English
Cited by
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