On connections between hypergraphs and algebras

Konrad Pióro

Displaying similar documents to “On connections between hypergraphs and algebras”

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...

Weak subalgebra lattices

Wiktor Bartol (1990)

Commentationes Mathematicae Universitatis Carolinae

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A duality between unary algebras and their subuniverse lattices

Bordalo, G. (1989)

Portugaliae mathematica

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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...