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

On subalgebra lattices of a finite unary algebra. II.

Konrad Pióro (2001)

Mathematica Bohemica

Similarity:

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

Similarity:

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...

The subalgebra lattice of a finite algebra

Konrad Pióro (2014)

Open Mathematics

Similarity:

The aim of this paper is to characterize pairs (L, A), where L is a finite lattice and A a finite algebra, such that the subalgebra lattice of A is isomorphic to L. Next, necessary and sufficient conditions are found for pairs of finite algebras (of possibly distinct types) to have isomorphic subalgebra lattices. Both of these characterizations are particularly simple in the case of distributive subalgebra lattices. We do not restrict our attention to total algebras only, but we consider...