The minimal closed monoids for the Galois connection End - Con

Danica Jakubíková-Studenovská; Reinhard Pöschel; Sándor Radelecki

Mathematica Bohemica (2024)

  • Volume: 149, Issue: 3, page 295-303
  • ISSN: 0862-7959

Abstract

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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 ) .

How to cite

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Jakubíková-Studenovská, Danica, Pöschel, Reinhard, and Radelecki, Sándor. "The minimal closed monoids for the Galois connection ${\rm End}$-${\rm Con}$." Mathematica Bohemica 149.3 (2024): 295-303. <http://eudml.org/doc/299561>.

@article{Jakubíková2024,
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 $\{\rm Quord\} (A,F)$.},
author = {Jakubíková-Studenovská, Danica, Pöschel, Reinhard, Radelecki, Sándor},
journal = {Mathematica Bohemica},
keywords = {endomorphism monoid; congruence lattice; quasiorder lattice; finite algebra},
language = {eng},
number = {3},
pages = {295-303},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The minimal closed monoids for the Galois connection $\{\rm End\}$-$\{\rm Con\}$},
url = {http://eudml.org/doc/299561},
volume = {149},
year = {2024},
}

TY - JOUR
AU - Jakubíková-Studenovská, Danica
AU - Pöschel, Reinhard
AU - Radelecki, Sándor
TI - The minimal closed monoids for the Galois connection ${\rm End}$-${\rm Con}$
JO - Mathematica Bohemica
PY - 2024
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 149
IS - 3
SP - 295
EP - 303
AB - 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 ${\rm Quord} (A,F)$.
LA - eng
KW - endomorphism monoid; congruence lattice; quasiorder lattice; finite algebra
UR - http://eudml.org/doc/299561
ER -

References

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  2. Halušková, E., 10.21136/MB.2019.0128-18, Math. Bohem. 145 (2020), 401-414. (2020) Zbl1499.08011MR4221842DOI10.21136/MB.2019.0128-18
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  7. Jakubíková-Studenovská, D., Pöschel, R., Radeleczki, S., 10.1007/s00012-018-0486-z, Algebra Univers. 79 (2018), Article ID 4, 23 pages. (2018) Zbl1414.08001MR3770896DOI10.1007/s00012-018-0486-z
  8. Jakubíková-Studenovská, D., Pöschel, R., Radeleczki, S., The structure of the maximal congruence lattices of algebras on a finite set, J. Mult.-Val. Log. Soft Comput. 36 (2021), 299-320. (2021) Zbl07536105MR4578804
  9. Janičková, L., 10.1007/s00012-022-00786-1, Algebra Univers. 83 (2022), Article ID 36, 10 pages. (2022) Zbl07573924MR4462594DOI10.1007/s00012-022-00786-1
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