Diameter and girth of Torsion Graph
2014 ◽
Vol 22
(3)
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pp. 127-136
AbstractLet R be a commutative ring with identity. Let M be an R-module and T (M)* be the set of nonzero torsion elements. The set T(M)* makes up the vertices of the corresponding torsion graph, ΓR(M), with two distinct vertices x, y ∈ T(M)* forming an edge if Ann(x) ∩ Ann(y) ≠ 0. In this paper we study the case where the graph ΓR(M) is connected with diam(ΓR(M)) ≤ 3 and we investigate the relationship between the diameters of ΓR(M) and ΓR(R). Also we study girth of ΓR(M), it is shown that if ΓR(M) contains a cycle, then gr(ΓR(M)) = 3.
1967 ◽
Vol 63
(3)
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pp. 569-578
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2020 ◽
Vol 17
(2)
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pp. 552-555
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1983 ◽
Vol 26
(3)
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pp. 267-270
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2019 ◽
Vol 18
(07)
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pp. 1950137
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2011 ◽
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(03)
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pp. 573-595
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2015 ◽
Vol 15
(01)
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pp. 1650014
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