ISOMORPHISMS ON ANNIHILATOR GRAPH OF MODULES
Publish place: The first national conference on intelligent systems, soft computing and applied mathematics
Publish Year: 1401
نوع سند: مقاله کنفرانسی
زبان: English
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شناسه ملی سند علمی:
FSSAC01_024
تاریخ نمایه سازی: 8 آذر 1402
Abstract:
Let R be a commutative ring with identity, and M be an R-module. In [۱], we focus on annihilator graph of modules, AG(M), the setT(M)* is a non-zero torsion elements of M —would be the vertices of annihilator graph of modules, and x, y ∈ T(M)* were adjacent if and only if AnnR ([x M]y)≠ AnnR (x) ∪ AnnR (y) or AnnR ([y : M]x) ≠ AnnR (x) ∪ AnnR (y). We investigate the structure, the diameter, and the girth of annihilator graph of R-modules [۱]. Ghalandarzadeh and Malakooti Rad in [۱۲] proved that for torsion graph of an R-module M is Γ(M) whose vertices are nonzero torsion elements of M, and two distinct vertices x and y are adjacent if and only if [x : M][y : M]M = {۰𝑀 }, if S = R\Z(M), then Γ(M) and Γ(𝑆 −۱M) are isomorphic for a multiplication R-module M. The purpose of this paper is to study the connection between the AG(M) and AG(𝑆 −۱M). We show that if S = R\Z(M), then AG(M) and AG(𝑆 −۱M) are isomorphic for a multiplication R-module M.
Authors
ZAHRA ABDOLLAH
Department of Mathematics, Qazvin Branch, Islamic Azad University, Qazvin, Iran
PARASTOO MALAKOOTI RAD
Department of Mathematics, Qazvin Branch, Islamic Azad University, Qazvin, Iran
PARVIN SAFARI
Department of Mathematics, Qazvin Branch, Islamic Azad University, Qazvin, Iran