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arXiv · 2010.06924

On the problem of the finiteness of the compressed zero divisor graphs of Artinian rings

Ganesh S. Kadu
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Abstract

Let R be an Artinian ring and G be the compressed zero-divisor graph associated to R. The question of when the clique number of compressed zero-divisor graphs is finite was raised by J. Coykendall, S. Sather-Wagstaff, L. Sheppardson, and S. Spiroff, in their survey paper entitled On Zero-divisor Graphs. They proved that if length of R is at most four then the clique number is finite. In the length six case they gave an example of a ring where the clique is infinite. In this paper we show that when length of ring is five then the clique number of compressed zero-divisor graph is finite.

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Ganesh S. Kadu. 2020-10-14. On the problem of the finiteness of the compressed zero divisor graphs of Artinian rings. https://arxiv.org/abs/2010.06924

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