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Some properties of the weak subalgebra lattice of a partial algebra of a fixed type. (English) Zbl 1069.08002

Summary: We investigate the case 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 form a directed hypergraph of a fixed type. It is shown that it is enough to consider some special hypergraphs. Finally, translating the results into 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.

MSC:

08A55 Partial algebras
08A30 Subalgebras, congruence relations
05C65 Hypergraphs
06B10 Lattice ideals, congruence relations
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