|
|||||
|
|
|
|
|
|
|
|
|
On zero-divisor
graphs of Boolean rings
Ali Mohammadian |
|
Vol. 251 (2011), No. 2, 375–383
|
Abstract |
|
The zero-divisor graph of a ring R is the graph whose vertices consist of the nonzero zero-divisors of R in which two distinct vertices a and b are adjacent if and only if either ab = 0 or ba = 0. In this paper, we investigate some properties of zero-divisor graphs of Boolean rings. Among other results, we prove that for any two rings R and S with Γ(R) ≃ Γ(S), if R is Boolean and |R| > 4, then R ≃ S. |
Keywords
Boolean ring, reduced ring, zero-divisor graph
|
Mathematical Subject Classification 2000
Primary: 05C25, 06E20, 16P10
|
Milestones
Received: 5 June 2010
Revised: 31 August 2010
Accepted: 7 September 2010
Published: 3 June 2011
Proposed: Alexander S. Merkurjev
|
Authors |
| Ali Mohammadian | |
| School of Mathematics Institute for Research in Fundamental Sciences (IPM) Niavaran Square P.O. Box 19395-5746 Tehran Iran |
|
|
