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Keywords:
endomorphism monoid; congruence lattice; quasiorder lattice; finite algebra
endomorphism monoid; congruence lattice; quasiorder lattice; finite algebra
Summary:
The minimal nontrivial endomorphism monoids $M={\rm End}{\rm Con} (A,F)$ of congruence lattices of algebras $(A,F)$ defined on a finite set $A$ are described. They correspond (via the Galois connection ${\rm End}$-${\rm Con}$) to the maximal nontrivial congruence lattices ${\rm Con} (A,F)$ investigated and characterized by the authors in previous papers. Analogous results are provided for endomorphism monoids of quasiorder lattices ${\rm Quord} (A,F)$.
References:
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