Critical 3-hypergraphs (detailed version)
Abderrahim Boussairi, Brahim Chergui, Pierre Ille, Mohamed Zaidi

TL;DR
This paper characterizes critical 3-hypergraphs, a class of hypergraphs where removing any vertex results in a non-prime hypergraph, expanding understanding of their structure and properties.
Contribution
It provides a complete characterization of critical 3-hypergraphs, a class previously not fully understood, based on the properties of modules and primeness.
Findings
Critical 3-hypergraphs are fully characterized.
Critical 3-hypergraphs have specific structural properties.
The results extend the theory of hypergraph modules and primeness.
Abstract
Given a 3-hypergraph , a subset of is a module of if for each such that and , there exists such that and for every , we have . For example, , and , where , are modules of , called trivial. A 3-hypergraph is prime if all its modules are trivial. Furthermore, a prime 3-hypergraph is critical if all its induced subhypergraphs, obtained by removing one vertex, are not prime. We characterize the critical 3-hypergraphs.
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Taxonomy
TopicsRings, Modules, and Algebras · Fuzzy and Soft Set Theory · Advanced Topology and Set Theory
