Residual Division Graph of Lattice Modules. (7th February 2022)

• Record Type: Journal Article
• Authors: Gandal, Ganesh; Jothi, R. Mary; Phadatare, Narayan
• Other Names: Tartarone Francesca Academic Editor.
• Is Part Of: Journal of mathematics. Volume 2022(2022)
• Publication Date: 2022-02-07
• Subjects: Mathematics -- Periodicals; Mathematics; Periodicals; 510
• DOI: 10.1155/2022/2892841
• Languages: English
• ISSNs: 2314-4629

Abstract

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 0 M ≠ P ∈ M such that N P = 0 M and two vertices N 1, N 2 are adjacent if N 1 N 2 = 0 M (where N 1 N 2 = N 1 : I M N 2 : I M I M ). It is proved that such a graph with the greatest element I M 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 R G M is isomorphic to a subgraph of Zariski topology graph Ģ X M with respect to X .