SOME PROPERTIES OF A COMMUTATIVE RING AND MULTIPLICATION MODULES OVER ZERO DIVISOR GRAPH
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...
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| Format: | Theses |
| Language: | Indonesia |
| Online Access: | https://digilib.itb.ac.id/gdl/view/19968 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | 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) |
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