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Planarity of Intersection Graph of Submodules of A Module
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نویسنده
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Malakooti P.
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منبع
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International Journal Of Industrial Mathematics - 2017 - دوره : 9 - شماره : 3 - صفحه:225 -229
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چکیده
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Let r be a commutative ring with identity and m be an unitary r-module. the intersection graph of an r-module m, denoted by γ(m), is a simple graph whose vertices are all non-trivial submodules of m and two distinct vertices n1 and n2 are adjacent if and only if n1 ∩ n2 ̸= 0. in this article, we investigate the concept of a planar intersection graph and maximal submodules of an r-module. in particular, we show that if γ(m) is a planar graph, then m ∼= m1 ⊕m2 for a multiplication r-module m with |m ax(m)|̸= 1.
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کلیدواژه
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Interval Methods; Multiplication Modules; Planar Graph; Module Theory; Torsion Graphs
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آدرس
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Islamic Azad University, Qazvin Branch, Department Of Mathematics, ایران
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پست الکترونیکی
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pmalakoti@gmail.com
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Authors
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