Displaying similar documents to “On subalgebra lattices of a finite unary algebra. II.”

On subalgebra lattices of a finite unary algebra. I.

Konrad Pióro (2001)

Mathematica Bohemica

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One of the main aims of the present and the next part [15] is to show that the theory of graphs (its language and results) can be very useful in algebraic investigations. We characterize, in terms of isomorphisms of some digraphs, all pairs 〈 𝐀 , 𝐋 〉 , where 𝐀 is a finite unary algebra and L a finite lattice such that the subalgebra lattice of 𝐀 is isomorphic to 𝐋 . Moreover, we find necessary and sufficient conditions for two arbitrary finite unary algebras to have isomorphic subalgebra lattices....

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 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,...