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Rings having zero-divisor graphs of small diameter or large girth

Published online by Cambridge University Press:  17 April 2009

S. B. Mulay
S. B. Mulay
Affiliation:
Department of Mathematics, The University of Tennessee, Knoxville, TN 37996, United States of America, e-mail: mulay@math.utk.edu
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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.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 72 , Issue 3 , December 2005 , pp. 481 - 490
Copyright
Copyright © Australian Mathematical Society 2005

References

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