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- W2998995768 abstract "Let R be a commutative ring with unity. The ring R consider as a simple graph whose vertices are the elements of R with two distinct vertices x and y are adjacent if xy=0 in R, where 0 is the zero element of R. In 1988 [3], I. Beck raised the conjecture that the chromatic number and clique number are same in any commutative ring with unity. In 1993 [1], Anderson and Naseer disproved the conjecture by giving a counter example of the conjecture. In this paper, we find the clique number and bounds for chromatic number of the finite product of commutative rings with unity in terms of its factors. As a consequence of our results, we construct infinitely many counter examples of rings of the above conjecture and some of the main results, proved by I. Beck in 1988 [3] and Anderson and Naseer in 1993 [1], are consequences of our results." @default.
- W2998995768 created "2020-01-23" @default.
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- W2998995768 date "2019-12-21" @default.
- W2998995768 modified "2023-09-27" @default.
- W2998995768 title "Istvan Beck Coloring of Commutative Rings with Unity" @default.
- W2998995768 hasPublicationYear "2019" @default.
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