SOME NON-CHROMATIC RINGS

Let R be a commutative ring with identity. Consider R as a simple grap h with vertices elements of R where any two distinct elements x, y is an element of R are adjacent if and only if xy = 0. Bect [2] conjectur ed that chi(R) = Cl(R), for all colorings R. Anderson and Naseer [1] p rovided a counter example to the conjecture i.e., gave an example of a non-chromatic ring. This paper generalizes the example and gives a la rge class of non-chromatic rings [Theorem 1.1]. A detailed analysis of the graph of these rings is also provided.