| Title:
|
Homomorphisms of algebras (English) |
| Author:
|
Novotný, Miroslav |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
52 |
| Issue:
|
2 |
| Year:
|
2002 |
| Pages:
|
345-364 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A construction of all homomorphisms of an algebra with a finite number of operations into an algebra of the same type is presented that consists in replacing algebras by suitable mono-unary algebras (possibly with some nullary operations) and their homomorphisms by suitable homomorphisms of the corresponding mono-unary algebras. Since a construction of all homomorphisms between two mono-unary algebras is known (see, e.g., [6], [7], [8]), a construction of all homomorphisms of an arbitrary algebra with a finite number of operations into an algebra of the same type can be described. (English) |
| Keyword:
|
algebra |
| Keyword:
|
mono-unary algebra |
| Keyword:
|
homomorphism of algebras |
| Keyword:
|
$m$-decomposable mapping |
| Keyword:
|
mono-unary algebra with one acceptable and several nullary operations |
| Keyword:
|
mono-unary algebra with one binding and several nullary operations |
| MSC:
|
08A02 |
| MSC:
|
08A60 |
| MSC:
|
08A62 |
| MSC:
|
18B10 |
| MSC:
|
18B99 |
| idZBL:
|
Zbl 1010.08004 |
| idMR:
|
MR1905442 |
| . |
| Date available:
|
2009-09-24T10:51:42Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127723 |
| . |
| Reference:
|
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| Reference:
|
[2] F. Gécseg and L. Peák: Algebraic Theory of Automata.Akadémiai Kiadó, Budapest, 1972. MR 0332374 |
| Reference:
|
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| Reference:
|
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| Reference:
|
[5] R. Mc Kenzie, G. F. Mc Nulty and W. S.Taylor: Algebras, Lattices, Varieties. Vol. I.Wadsworth and Brooks/Cole, Monterey, 1987. |
| Reference:
|
[6] M. Novotný: O jednom problému z teorie zobrazení (Sur un problème de la théorie des applications).Publ. Fac. Sci. Univ. Masaryk Brno No. 344, 1953, pp. 53–64. |
| Reference:
|
[7] M. Novotný: Über Abbildungen von Mengen.Pac. J. Math. 13 (1963), 1359–1369. MR 0157143 |
| Reference:
|
[8] M. Novotný: Mono-unary algebras in the work of Czechoslovak mathematicians.Arch. Math. (Brno) 26 (1990), 155–164. MR 1188275 |
| Reference:
|
[9] M. Novotný: Construction of all strong homomorphisms of binary structures.Czechoslovak Math. J. 41 (116) (1991), 300–311. MR 1105447 |
| Reference:
|
[10] M. Novotný: Ternary structures and groupoids.Czechoslovak Math. J. 41 (116) (1991), 90–98. MR 1087627 |
| Reference:
|
[11] M. Novotný: On some correspondences between relational structures and algebras.Czechoslovak Math. J. 43 (118) (1993), 643–647. MR 1258426 |
| Reference:
|
[12] M. Novotný: Construction of all homomorphisms of groupoids.Czechoslovak Math. J. 46 (121) (1996), 141–153. MR 1371696 |
| Reference:
|
[13] M. Novotný: Construction of all homomorphisms of mono-$n$-ary algebras.Czechoslovak Math. J. 46 (121) (1996), 331–333. MR 1388621 |
| Reference:
|
[14] M. Novotný: Homomorphisms and strong homomorphisms of relational structures.Arch. Math. (Brno) 33 (1997), 57–64. MR 1464301 |
| Reference:
|
[15] M. Novotný: Homomorphisms of algebraic structures.In: Proceedings of the 11th International Scientific Conference VUT Brno, Faculty of Civil Engineering, Oct. 18–20, 1999, Section Applied Mathematics, (eds.), , pp. 13–20. MR 1696667 |
| Reference:
|
[16] A. Pultr and V. Trnková: Combinatorial, Algebraic and Topological Representations of Groups, Semigroups and Categories.Academia, Prague, 1980. () MR 0563525 |
| Reference:
|
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| . |
