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Some properties of the weak subalgebra lattice of a partial algebra of
a fixed type

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*Konrad Pioro*

**Address.** Institute of Mathematics, Warsaw University, ul. Banacha
2, PL-02-097, Warsaw, POLAND
**E-mail:** kpioro@mimuw.edu.pl

**Abstract.** 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.

**AMSclassification.** 05C65, 05C99, 08A30, 08A55 (05C90, 06B15,
06D05).

**Keywords.** Hypergraph, weak subalgebra, weak subalgebra lattice,
partial algebra.