Zero-Divisor Graphs and Zero-Divisor Functors
| Autor: | Enrico Sbarra, Maurizio Zanardo |
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| Rok vydání: | 2022 |
| Předmět: | |
| DOI: | 10.48550/arxiv.2203.02952 |
| Popis: | 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. Comment: 18 pages, 5 figures. Submitted to "Journal of Algebra" (Manuscript Number: JALGEBRA-D-22-00137) |
| Databáze: | OpenAIRE |
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