Displaying similar documents to “On some non-obvious connections between graphs and unary partial algebras”

On connections between hypergraphs and algebras

Konrad Pióro (2000)

Archivum Mathematicum

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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,...

On subalgebra lattices of a finite unary algebra. II.

Konrad Pióro (2001)

Mathematica Bohemica

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We use graph-algebraic results proved in [8] and some results of the graph theory to characterize all pairs 〈 𝐋 1 , 𝐋 2 〉 of lattices for which there is a finite partial unary algebra such that its weak and strong subalgebra lattices are isomorphic to 𝐋 1 and 𝐋 2 , respectively. Next, we describe other pairs of subalgebra lattices (weak and relative, etc.) of a finite unary algebra. Finally, necessary and sufficient conditions are found for quadruples 〈 𝐋 1 , 𝐋 2 , 𝐋 3 , 𝐋 4 〉 of lattices for which there is a finite unary algebra...