| Title:
|
The minimal closed monoids for the Galois connection ${\rm End}$-${\rm Con}$ (English) |
| Author:
|
Jakubíková-Studenovská, Danica |
| Author:
|
Pöschel, Reinhard |
| Author:
|
Radeleczki, Sándor |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
149 |
| Issue:
|
3 |
| Year:
|
2024 |
| Pages:
|
295-303 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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 ${\rm Quord} (A,F)$. (English) |
| Keyword:
|
endomorphism monoid |
| Keyword:
|
congruence lattice |
| Keyword:
|
quasiorder lattice |
| Keyword:
|
finite algebra |
| MSC:
|
08A30 |
| MSC:
|
08A35 |
| MSC:
|
08A60 |
| DOI:
|
10.21136/MB.2023.0133-22 |
| . |
| Date available:
|
2024-09-11T13:44:27Z |
| Last updated:
|
2024-09-11 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/152535 |
| . |
| Reference:
|
[1] Halušková, E.: Strong endomorphism kernel property for monounary algebras.Math. Bohem. 143 (2018), 161-171. Zbl 1463.08003, MR 3831484, 10.21136/MB.2017.0056-16 |
| Reference:
|
[2] Halušková, E.: Some monounary algebras with EKP.Math. Bohem. 145 (2020), 401-414. Zbl 1499.08011, MR 4221842, 10.21136/MB.2019.0128-18 |
| Reference:
|
[3] Jakubíková-Studenovská, D.: On congruence relations of monounary algebras I.Czech. Math. J. 32 (1982), 437-459. Zbl 0509.08003, MR 0669786, 10.21136/CMJ.1982.101820 |
| Reference:
|
[4] Jakubíková-Studenovská, D.: On congruence relations of monounary algebras II.Czech. Math. J. 33 (1983), 448-466. Zbl 0535.08003, MR 0718928, 10.21136/CMJ.1983.101895 |
| Reference:
|
[5] Jakubíková-Studenovská, D., Pócs, J.: Monounary Algebras.P. J. Šafárik University, Košice (2009). Zbl 1181.08001 |
| Reference:
|
[6] Jakubíková-Studenovská, D., Pöschel, R., Radeleczki, S.: The lattice of quasiorder lattices of algebras on a finite set.Algebra Univers. 75 (2016), 197-220. Zbl 1338.08005, MR 3515397, 10.1007/s00012-016-0373-4 |
| Reference:
|
[7] Jakubíková-Studenovská, D., Pöschel, R., Radeleczki, S.: The lattice of congruence lattices of algebras on a finite set.Algebra Univers. 79 (2018), Article ID 4, 23 pages. Zbl 1414.08001, MR 3770896, 10.1007/s00012-018-0486-z |
| Reference:
|
[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. Zbl 07536105, MR 4578804 |
| Reference:
|
[9] Janičková, L.: Monounary algebras containing subalgebras with meet-irreducible congruence lattice.Algebra Univers. 83 (2022), Article ID 36, 10 pages. Zbl 07573924, MR 4462594, 10.1007/s00012-022-00786-1 |
| Reference:
|
[10] Länger, H., Pöschel, R.: Relational systems with trivial endomorphisms and polymorphisms.J. Pure Appl. Algebra 32 (1984), 129-142. Zbl 0558.08004, MR 0741962, 10.1016/0022-4049(84)90048-3 |
| Reference:
|
[11] Pálfy, P. P.: Unary polynomials in algebras. I.Algebra Univers. 18 (1984), 262-273. Zbl 0546.08005, MR 0745492, 10.1007/BF01203365 |
| Reference:
|
[12] Quackenbush, R., Wolk, B.: Strong representation of congruence lattices.Algebra Univers. 1 (1971), 165-166. Zbl 0231.06006, MR 0295980, 10.1007/BF02944974 |
| . |
