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On some finite groupoids with distributive subgroupoid lattices

Konrad Pióro (2002)

Discussiones Mathematicae - General Algebra and Applications

The aim of the paper is to show that if S(G) is distributive, and also G satisfies some additional condition, then the union of any two subgroupoids of G is also a subgroupoid (intuitively, G has to be in some sense a unary algebra).

On subalgebra lattices of a finite unary algebra. II.

Konrad Pióro (2001)

Mathematica Bohemica

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 having...

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