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arXiv · 1807.11283

Categorial properties of compressed zero-divisor graphs of finite commutative rings

Alen Đurić·Sara Jevđenić·Nik Stopar
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Abstract

We define a compressed zero-divisor graph $\varTheta(K)$ of a finite commutative unital ring $K$, where the compression is performed by means of the associatedness relation. We prove that this is the best possible compression which induces a functor $\varTheta$, and that this functor preserves categorial products (in both directions). We use the structure of $\varTheta(K)$ to characterize important classes of finite commutative unital rings, such as local rings and principal ideal rings.

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Alen Đurić, Sara Jevđenić, Nik Stopar. 2018-07-30. Categorial properties of compressed zero-divisor graphs of finite commutative rings. https://doi.org/10.1142/s0219498821500699

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