Given a 3-uniform hypergraph H, a subset M of V(H) is a module of H if for each \(e\in E(H)\) such that \(e\cap M\ne \emptyset\) and \(e\setminus M\ne \emptyset\), there exists \(m\in M\) such that \(e\cap M=\{m\}\) and for every \(n\in M\), we have \((e\setminus \{m\})\cup \{n\}\in E(H)\). For example, \(\emptyset\), V(H) and \(\{v\}\), where \(v\in V(H)\), are modules of H, called trivial. A 3-uniform hypergraph is prime if all its modules are trivial. Given a prime 3-uniform hypergraph, we study its prime, 3-uniform and induced subhypergraphs. Our main result is: given a prime 3-uniform hypergraph H, with \(|V(H)|\ge 4\), there exist \(v,w\in V(H)\) such that \(H-\{v,w\}\) is prime.

给定一个3一致超ħ，子集中号的V（ħ）是一个模块ħ如果对于每个\（E \于E（H）\） ，使得\（E \帽中号\ NE \ emptyset \）和\(e\setminus M\ne \emptyset\)，存在\(m\in M\)使得\(e\cap M=\{m\}\)并且对于每个\(n\in M\)，我们有\((e\setminus \{m\})\cup \{n\}\in E(H)\)。例如，\(\emptyset\)、V ( H ) 和\(\{v\}\)，其中\(v\in V(H)\)是H 的模块，称为琐碎。一个 3-均匀超图是素数，如果它的所有模块都是平凡的。给定一个素数 3-uniform 超图，我们研究它的素数、3-uniform 和诱导子超图。我们的主要结果是：给定一个素数 3-均匀超图H，具有\(|V(H)|\ge 4\)，存在\(v,w\in V(H)\)使得\(H- \{v,w\}\)是素数。