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arXiv · 2203.02952

Zero-Divisor Graphs and Zero-Divisor Functors

Enrico Sbarra·Maurizio Zanardo
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Abstract

Inspired by a very recent work of A. {\DH}uri\'c, S. Jev{\dj}eni\'c and N. Stopar, we introduce a new definition of zero-divisor graphs attached to rings, that includes all of the classical definitions already known in the literature. We provide an interpretation of such graphs as images of a functor, that we call zero-divisor functor and which is associated with a family of special equivalence relations fixed beforehand. We thus recover and generalize many known results for zero-divisor graphs and provide a framework which might be useful for further investigations on this topic.

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Enrico Sbarra, Maurizio Zanardo. 2022-03-06. Zero-Divisor Graphs and Zero-Divisor Functors. https://arxiv.org/abs/2203.02952

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