Prime 3-Uniform Hypergraphs

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