Displaying similar documents to “On some unary algebras and their subalgebra lattices”

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 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 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...