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The minimal closed monoids for the Galois connection End - Con

Danica Jakubíková-Studenovská, Reinhard Pöschel, Sándor Radelecki (2024)

Mathematica Bohemica

The minimal nontrivial endomorphism monoids M = End Con ( A , F ) of congruence lattices of algebras ( A , F ) defined on a finite set A are described. They correspond (via the Galois connection End - Con ) to the maximal nontrivial congruence lattices Con ( A , F ) investigated and characterized by the authors in previous papers. Analogous results are provided for endomorphism monoids of quasiorder lattices Quord ( A , F ) .

The subalgebra lattice of a finite algebra

Konrad Pióro (2014)

Open Mathematics

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 the more...

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