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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(Γ(M)) with vertices all elements of M, and two distinct vertices m and n are adjacent if and only if m + n ∈ T(M).
In this paper, we study the basic properties and possible structures of two (induced) subgraphs Tσr0 (Γ(M)) and T0 (Γ(M)) of T(Γ(M)), with vertices T(M) ＼ {0} and M ＼ {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.
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참고문헌 (15)
참고문헌 신청
A. Abbasi / 2012 / The total graph of a module over a commutative ring with respect to proper submodules / J. Algebra Appl 11 (3) : 13 ~
Ahmad Abbasi / 2012 / The total graph of a commutative ring with respect to proper ideals / 대한수학회지 49 (1) : 85 ~ 98
D. D. Anderson / 1993 / Beck's coloring of a commutative ring / J. Algebra 159 (2) : 500 ~ 514
D. D. Anderson / 2014 / The set of torsion elements of a module / Comm. Algebra 42 : 1835 ~ 1843
D. F. Anderson / 1999 / zero-divisor graph of a commutative ring / J. Algebra 217 (2) : 437 ~ 447
Ahmad Abbasi / 2012 / The total graph of a commutative ring with respect to proper ideals / 대한수학회지 49 (1) : 85 ~ 98
D. D. Anderson / 1993 / Beck's coloring of a commutative ring / J. Algebra 159 (2) : 500 ~ 514
D. D. Anderson / 2014 / The set of torsion elements of a module / Comm. Algebra 42 : 1835 ~ 1843
D. F. Anderson / 1999 / zero-divisor graph of a commutative ring / J. Algebra 217 (2) : 437 ~ 447
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