SOME PROPERTIES OF A COMMUTATIVE RING AND MULTIPLICATION MODULES OVER ZERO DIVISOR GRAPH

• Main Author: HARIANTO (NIM : 20113076 ), BUDI
• Format: Theses
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/19968
• Institution: Institut Teknologi Bandung

For a commutative ring with set of zero divisors Z(R), the zero divisors graph Г(R) = Z{R }, with distinct x and y adjacent if and only if xy = 0. The annihilator ideal-based zero divisor graph Г Ann (M) (R) is a simple graph, whose vertices are the set {α € R Ann (M) | abM = 0. For same b € R Ann (M}, where distinct a and b adjacent if and only if . In this thesis, we show that if Г (R) is complete graph if and only if R ͇~Z2 x Z2 or x, y = 0 for all x,y € Z (R) . we also examine some properties of an R-module over a von Neumann regular rings, and properties of an multiplication -module over complete graph Г Ann (M) (R)