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On connections between hypergraphs and algebras
Archivum mathematicum, Tome 36 (2000) no. 1, pp. 45-60 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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The aim of the present paper is to translate some algebraic concepts to hypergraphs. Thus we obtain a new language, very useful in the investigation of subalgebra lattices of partial, and also total, algebras. In this paper we solve three such problems on subalgebra lattices, other will be solved in [[Pio4]]. First, we show that for two arbitrary partial algebras, if their directed hypergraphs are isomorphic, then their weak, relative and strong subalgebra lattices are isomorphic. Secondly, we prove that two partial algebras have isomorphic weak subalgebra lattices iff their hypergraphs are isomorphic. Thirdly, for an arbitrary lattice $\mathbf {L}$ and a partial algebra $\mathbf {A}$ we describe (necessary and sufficient conditions) when the weak subalgebra lattice of $\mathbf {A}$ is isomorphic to $\mathbf {L}$.
The aim of the present paper is to translate some algebraic concepts to hypergraphs. Thus we obtain a new language, very useful in the investigation of subalgebra lattices of partial, and also total, algebras. In this paper we solve three such problems on subalgebra lattices, other will be solved in [[Pio4]]. First, we show that for two arbitrary partial algebras, if their directed hypergraphs are isomorphic, then their weak, relative and strong subalgebra lattices are isomorphic. Secondly, we prove that two partial algebras have isomorphic weak subalgebra lattices iff their hypergraphs are isomorphic. Thirdly, for an arbitrary lattice $\mathbf {L}$ and a partial algebra $\mathbf {A}$ we describe (necessary and sufficient conditions) when the weak subalgebra lattice of $\mathbf {A}$ is isomorphic to $\mathbf {L}$.
Classification : 05C65, 05C90, 08A30, 08A55
Keywords: hypergraph; subalgebras (relative; strong; weak); subalgebra lattices; partial algebra 
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Pióro, Konrad. On connections between hypergraphs and algebras. Archivum mathematicum, Tome 36 (2000) no. 1, pp. 45-60. http://geodesic.mathdoc.fr/item/ARM_2000_36_1_a5/

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