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Residual Division Graph of Lattice Modules

Author

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  • Ganesh Gandal
  • R. Mary Jothi
  • Narayan Phadatare
  • Francesca Tartarone

Abstract

Let L be a multiplicative lattice and M be a lattice module over L. In this paper, we assign a graph to M called residual division graph RG(M) in which the element N∈M is a vertex if there exists 0M≠P∈M such that NP=0M and two vertices N1,N2 are adjacent if N1N2=0M (where N1N2=N1:IMN2:IMIM). It is proved that such a graph with the greatest element IM which does not belong to the vertex set is nonempty if and only if M is a prime lattice module. Also, we provide conditions such that RGM is isomorphic to a subgraph of Zariski topology graph ĢXM with respect to X.

Suggested Citation

  • Ganesh Gandal & R. Mary Jothi & Narayan Phadatare & Francesca Tartarone, 2022. "Residual Division Graph of Lattice Modules," Journal of Mathematics, Hindawi, vol. 2022, pages 1-6, February.
    • Handle: RePEc:hin:jjmath:2892841
    DOI: 10.1155/2022/2892841
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