PLANARITY OF INTERSECTION GRAPH OF SUBMODULES OF A MODULE

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MALAKOOTI P.

مرکز اطلاعات علمی Scientific Information Database (SID) - Trusted Source for Research and Academic Resources

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Journal: INTERNATIONAL JOURNAL OF INDUSTRIAL MATHEMATICS Year:2017 | Volume:9 | Issue:3 Page(s): 225-229

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Information Journal Paper

Title

PLANARITY OF INTERSECTION GRAPH OF SUBMODULES OF A MODULE

Author(s)

MALAKOOTI P. | Issue Writer Certificate

Keywords

INTERVAL METHODSQ2

MULTIPLICATION MODULESQ2

PLANAR GRAPHQ2

MODULE THEORYQ2

TORSION GRAPHSQ2

Abstract

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 G (M), is a simple graph whose vertices are all non-trivial submodules ofM and two distinct vertices N 1 and N 2 are adjacent if and only if N 1 ÇN 2 ¹0. 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 G (M) is a PLANAR GRAPH, then M @M1 ÅM 2 for a multiplication R -module Mwith |Max (M)|¹1.

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APA: Copy

MALAKOOTI, P.. (2017). PLANARITY OF INTERSECTION GRAPH OF SUBMODULES OF A MODULE. INTERNATIONAL JOURNAL OF INDUSTRIAL MATHEMATICS, 9(3), 225-229. SID. https://sid.ir/paper/231793/en

Vancouver: Copy

MALAKOOTI P.. PLANARITY OF INTERSECTION GRAPH OF SUBMODULES OF A MODULE. INTERNATIONAL JOURNAL OF INDUSTRIAL MATHEMATICS[Internet]. 2017;9(3):225-229. Available from: https://sid.ir/paper/231793/en

IEEE: Copy

P. MALAKOOTI, “PLANARITY OF INTERSECTION GRAPH OF SUBMODULES OF A MODULE,” INTERNATIONAL JOURNAL OF INDUSTRIAL MATHEMATICS, vol. 9, no. 3, pp. 225–229, 2017, [Online]. Available: https://sid.ir/paper/231793/en

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