Annihilator Ideal-Based Zero-Divisor Graphs Over Multiplication Modules

2013 ◽  
Vol 41 (3) ◽  
pp. 1134-1148 ◽  
Author(s):  
Ghalandarzadeh ◽  
S. Shirinkam ◽  
P. Malakooti Rad
Keyword(s):  
Zero Divisor ◽  
Annihilator Ideal

scholarly journals On the diameter of the graph ГAnn(M)(R)

Filomat ◽  
2012 ◽  
Vol 26 (3) ◽  
pp. 623-629 ◽  
Author(s):  
David Anderson ◽  
Shaban Ghalandarzadeh ◽  
Sara Shirinkam ◽  
Parastoo Rad
Keyword(s):  
Commutative Ring ◽  
Complete Graph ◽  
Zero Divisor ◽  
Prime Ideals ◽  
Annihilator Ideal ◽  
Zero Divisor Graph ◽  
Minimal Prime ◽  
The Relationship ◽  
The Ideal

For a commutative ring R with identity, the ideal-based zero-divisor graph, denoted by ?I (R), is the graph whose vertices are {x ? R\I|xy ? I for some y ? R\I}, and two distinct vertices x and y are adjacent if and only if xy?I. In this paper, we investigate an annihilator ideal-based zero-divisor graph, denoted by ?Ann(M)(R), by replacing the ideal I with the annihilator ideal Ann(M) for an R-module M. We also study the relationship between the diameter of ?Ann(M) (R) and the minimal prime ideals of Ann(M). In addition, we determine when ?Ann(M)(R) is complete. In particular, we prove that for a reduced R-module M, ?Ann(M) (R) is a complete graph if and only if R ? Z2?Z2 and M ? M1?M2 for M1 and M2 nonzero Z2-modules.

THE CYLINDRICAL CROSSING NUMBER OF ZERO DIVISOR GRAPHS

2020 ◽  
Vol 9 (8) ◽  
pp. 5901-5908
Author(s):  
M. Sagaya Nathan ◽  
J. Ravi Sankar
Keyword(s):  
Zero Divisor ◽  
Crossing Number

Eigenvalues of zero divisor graphs of principal ideal rings

2021 ◽  
pp. 1-15
Author(s):  
Jitsupat Rattanakangwanwong ◽  
Yotsanan Meemark
Keyword(s):  
Principal Ideal ◽  
Zero Divisor

scholarly journals Correction to: Classification of non-local rings with genus two zero-divisor graphs

2021 ◽  
Vol 25 (4) ◽  
pp. 3355-3356
Author(s):  
T. Asir ◽  
K. Mano ◽  
T. Tamizh Chelvam
Keyword(s):  
Zero Divisor ◽  
Local Rings ◽  
Non Local ◽  
Genus Two

scholarly journals On the set of divisors with zero geometric defect

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Dinh Tuan Huynh ◽  
Duc-Viet Vu
Keyword(s):  
Line Bundle ◽  
Zero Divisor ◽  
Ample Line Bundle ◽  
Holomorphic Section ◽  
Projective Manifold ◽  
Holomorphic Curve ◽  
Very Ample Line Bundle ◽  
Complex Projective ◽  
Geometric Defect

AbstractLet {f:\mathbb{C}\to X} be a transcendental holomorphic curve into a complex projective manifold X. Let L be a very ample line bundle on {X.} Let s be a very generic holomorphic section of L and D the zero divisor given by {s.} We prove that the geometric defect of D (defect of truncation 1) with respect to f is zero. We also prove that f almost misses general enough analytic subsets on X of codimension 2.

scholarly journals The diameter of annihilator ideal graph of ℤn

2021 ◽  
Author(s):  
Ami Rahmawati ◽  
Vika Yugi Kurniawan ◽  
Supriyadi Wibowo
Keyword(s):  
Annihilator Ideal

scholarly journals Sub-semigroups determined by the zero-divisor graph

2008 ◽  
Vol 308 (22) ◽  
pp. 5122-5135 ◽  
Author(s):  
Tongsuo Wu ◽  
Dancheng Lu
Keyword(s):  
Zero Divisor ◽  
Zero Divisor Graph

Planar zero divisor graphs of partially ordered sets

2012 ◽  
Vol 137 (1-2) ◽  
pp. 27-35 ◽  
Author(s):  
M. Afkhami ◽  
Z. Barati ◽  
K. Khashyarmanesh
Keyword(s):  
Zero Divisor ◽  
Partially Ordered Sets ◽  
Ordered Sets ◽  
Partially Ordered
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