The minimal closed monoids for the Galois connection ${\rm End}$-${\rm Con}$

Abstract

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 ${\rm Quord} (A,F)$.

Keywords

• endomorphism monoid
• congruence lattice
• quasiorder lattice
• finite algebra