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.
| Item Type: | Article |
|---|---|
| Source: | Copyright of this article belongs to Taylor and Francis Ltd. |
| ID Code: | 3207 |
| Deposited On: | 11 Oct 2010 09:58 |
| Last Modified: | 18 May 2011 10:15 |
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