Bull. Austral. Math. Soc. 72(3) pp.481--490, 2005.
Rings having zero-divisor graphs of
small diameter or large girth
S.B. Mulay |
.
Abstract
Let R be a
commutative ring possessing (non-zero) zero-divisors. There is a
natural graph associated to the set of zero-divisors of
R. In this article we present a
characterisation of two types of R. Those for which the associated zero-divisor
graph has diameter different from 3 and
those R for which the associated
zero-divisor graph has girth other than 3. Thus, in a sense, for a generic non-domain
R the associated zero-divisor
graph has diameter 3 as well as girth
3.
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[an error occurred while processing this directive]| (Metadata: XML, RSS, BibTeX) | MathSciNet: MR2199650 | Z'blatt-MATH: 1097.13007 |
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ISSN 0004-9727