Geodesic
Some properties of the weak subalgebra lattice of a partial algebra of a fixed type
Archivum mathematicum, Tome 38 (2002) no. 2, pp. 81-94.

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We investigate, using results from [[p3]], when a given lattice is isomorphic to the weak subalgebra lattice of a partial algebra of a fixed type. First, we reduce this problem to the question when hyperedges of a hypergraph can be directed to a form of directed hypergraph of a fixed type. Secondly, we show that it is enough to consider some special hypergraphs. Finally, translating these results onto the lattice language, we obtain necessary conditions for our algebraic problem, and also, we completely characterize the weak subalgebra lattice for algebras of some types.
Classification : 05C65, 06B10, 06B15, 08A30, 08A55
Keywords: hypergraph; weak subalgebra; weak subalgebra lattice; partial algebra 
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     title = {Some properties of the weak subalgebra lattice of a partial algebra of a fixed type},
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Pióro, Konrad. Some properties of the weak subalgebra lattice of a partial algebra of a fixed type. Archivum mathematicum, Tome 38 (2002) no. 2, pp. 81-94. http://geodesic.mathdoc.fr/item/ARM_2002__38_2_a0/