Geodesic
The minimal closed monoids for the Galois connection ${\rm End}$-${\rm Con}$
Mathematica Bohemica, Tome 149 (2024) no. 3, pp. 295-303
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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 ${\rm Quord} (A,F)$.
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 ${\rm Quord} (A,F)$.
DOI : 10.21136/MB.2023.0133-22
Classification : 08A30, 08A35, 08A60
Keywords: endomorphism monoid; congruence lattice; quasiorder lattice; finite algebra 
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Jakubíková-Studenovská, Danica; Pöschel, Reinhard; Radeleczki, Sándor. The minimal closed monoids for the Galois connection ${\rm End}$-${\rm Con}$. Mathematica Bohemica, Tome 149 (2024) no. 3, pp. 295-303. doi: 10.21136/MB.2023.0133-22

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