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All Journal CAUCHY: Jurnal Matematika Murni dan Aplikasi
Purnamaadi, Dedy Zulkharnain
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Mathematics

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Correspondence Between Torsion and Annihilator Graph of Modules Zn Over Commutative Rings Andari, Ari; Mahanani, Dwi Mifta; Purnamaadi, Dedy Zulkharnain
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 10, No 1 (2025): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v10i1.30002

Abstract

Let M be a module over a commutative ring. Torsion graph of module M is a simple undirected graph where the vertices are nonzero torsion elements of M and two different vertices x and y is adjacent if intersection of Ann(x) and Ann(y) is not zero. Meanwhile, the annihilator graph of the module M is a simple undirected graph where the vertex set is Z_R(M)\Ann_R(M) and two different vertices x and y is adjacent if union of Ann_M(x) and Ann_M(y) is not equal with Ann_M(xy). In this paper, we focus on the discussion of torsion graph and annihilator graph for integer modulo n module Zn. Moreover, we obtain some relation between them based on the prime factorization of n.
Co-Authors Corina Karim, Ari Andari Dwi Mifta Mahanani, Dwi Mifta