Bhatwadekar, S. M. ; Dumaldar, Mahesh N. ; Sharma, Pramod K.
(1998)
*Some non-chromatic rings*
Communications in Algebra, 26
(2).
pp. 477-505.
ISSN 0092-7872

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Related URL: http://dx.doi.org/10.1080/00927879808826143

## Abstract

Let R be a commutative ring with identity. Consider R as a simple graph with vertices elements of R where any two distinct elements x, y ε R are adjacent if and only if xy = 0. Beck [2] conjectured that χ(R) =c1(R), for all colorings R. Anderson and Naseer [1] provided a counter example to the conjecture i.e., gave an example of a non-chromatic ring. This paper generalizes the example and gives a large class of non-chromatic rings [Theorem 1.1]. A detailed analysis of the graph of these rings is also provided.

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Deposited On: | 11 Oct 2010 09:58 |

Last Modified: | 18 May 2011 10:15 |

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