1. Beck's Coloring of Finite Product of Commutative Ring with Unity.
- Author
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Kavaskar, Thanthony
- Subjects
COMMUTATIVE rings ,FINITE, The ,ALGEBRA - Abstract
In 1988, Beck (J Algebra 116:208–226, 1988) conjectured that the chromatic number and clique number is the same for the graphs associated to any commutative ring with unity. In 1993, Anderson and Naseer (J Algebra 159:500–514, 1993) disproved the conjecture with a counterexample. In this paper, we find the clique number and bounds for the chromatic number of the graph associated with the finite product of commutative rings with unity. Also we show that some of the results, proved in (Anderson and Naseer in J Algebra 159:500–514, 1993, Beck in J Algebra 116:208–226, 1988) are consequences of our results. In addition, we have constructed a new family of counterexamples of the above conjecture. [ABSTRACT FROM AUTHOR]
- Published
- 2022
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