Zero-Divisor Graphs and Zero-Divisor Functors

2022/03/06 by Enrico Sbarra, Sbarra, Enrico, Maurizio Zanardo +1 · 1 citation
Mathematics · #05C25 (Primary) 18A30 #13P25 (Secondary) #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2203.02952

openalex publication_date 2022/03/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Inspired by a very recent work of A. Ðurić, S. Jevđenić 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.

Cited by

• On the diameter and girth of zero-divisor graphs of inverse semigroups

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