Displaying similar documents to “The weak subalgebra lattice of a unary partial algebra of a given infinite unary type”

On some non-obvious connections between graphs and unary partial algebras

Konrad Pióro (2000)

Czechoslovak Mathematical Journal

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In the present paper we generalize a few algebraic concepts to graphs. Applying this graph language we solve some problems on subalgebra lattices of unary partial algebras. In this paper three such problems are solved, other will be solved in papers [Pió I], [Pió II], [Pió III], [Pió IV]. More precisely, in the present paper first another proof of the following algebraic result from [Bar1] is given: for two unary partial algebras 𝐀 and 𝐁 , their weak subalgebra lattices are isomorphic...

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...

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,...