Geodesic
Homomorphisms of algebras
Czechoslovak Mathematical Journal, Tome 52 (2002) no. 2, pp. 345-364 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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.
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.
Classification : 08A02, 08A60, 08A62, 18B10, 18B99
Keywords: algebra; mono-unary algebra; homomorphism of algebras; $m$-decomposable mapping; mono-unary algebra with one acceptable and several nullary operations; mono-unary algebra with one binding and several nullary operations 
@article{CMJ_2002_52_2_a10,
     author = {Novotn\'y, Miroslav},
     title = {Homomorphisms of algebras},
     journal = {Czechoslovak Mathematical Journal},
     pages = {345--364},
     year = {2002},
     volume = {52},
     number = {2},
     mrnumber = {1905442},
     zbl = {1010.08004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2002_52_2_a10/}
}
TY  - JOUR
AU  - Novotný, Miroslav
TI  - Homomorphisms of algebras
JO  - Czechoslovak Mathematical Journal
PY  - 2002
SP  - 345
EP  - 364
VL  - 52
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/CMJ_2002_52_2_a10/
LA  - en
ID  - CMJ_2002_52_2_a10
ER  - 
%0 Journal Article
%A Novotný, Miroslav
%T Homomorphisms of algebras
%J Czechoslovak Mathematical Journal
%D 2002
%P 345-364
%V 52
%N 2
%U http://geodesic.mathdoc.fr/item/CMJ_2002_52_2_a10/
%G en
%F CMJ_2002_52_2_a10
Novotný, Miroslav. Homomorphisms of algebras. Czechoslovak Mathematical Journal, Tome 52 (2002) no. 2, pp. 345-364. http://geodesic.mathdoc.fr/item/CMJ_2002_52_2_a10/

[1] P. M. Cohn: Universal Algebra. Harper and Row, NewYork-Evanston-London, 1965. | MR | Zbl

[2] F. Gécseg and L. Peák: Algebraic Theory of Automata. Akadémiai Kiadó, Budapest, 1972. | MR

[3] J. E. Hopcroft and J. D. Ullman: Formal Languages and Their Relation to Automata. Addison-Wesley Publishing Company, Reading, 1969. | MR

[4] S. Mac Lane: Categories for the Working Mathematician. Springer, New York-Heidelberg-Berlin, 1971. | MR | Zbl

[5] R. Mc Kenzie, G. F. Mc Nulty and W. S.Taylor: Algebras, Lattices, Varieties. Vol. I. Wadsworth and Brooks/Cole, Monterey, 1987.

[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.

[7] M. Novotný: Über Abbildungen von Mengen. Pac. J.  Math. 13 (1963), 1359–1369. | MR

[8] M. Novotný: Mono-unary algebras in the work of Czechoslovak mathematicians. Arch. Math. (Brno) 26 (1990), 155–164. | MR

[9] M. Novotný: Construction of all strong homomorphisms of binary structures. Czechoslovak Math.  J. 41 (116) (1991), 300–311. | MR

[10] M. Novotný: Ternary structures and groupoids. Czechoslovak Math. J. 41 (116) (1991), 90–98. | MR

[11] M. Novotný: On some correspondences between relational structures and algebras. Czechoslovak Math. J. 43 (118) (1993), 643–647. | MR

[12] M. Novotný: Construction of all homomorphisms of groupoids. Czechoslovak Math.  J. 46 (121) (1996), 141–153. | MR

[13] M. Novotný: Construction of all homomorphisms of mono-$n$-ary algebras. Czechoslovak Math. J. 46 (121) (1996), 331–333. | MR

[14] M. Novotný: Homomorphisms and strong homomorphisms of relational structures. Arch. Math. (Brno) 33 (1997), 57–64. | MR

[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

[16] A. Pultr and V. Trnková: Combinatorial, Algebraic and Topological Representations of Groups, Semigroups and Categories. Academia, Prague, 1980. () | MR

[17] M. O. Rabin and D. Scott: Finite automata and their decision problems. IBM Journal 3 (1959), 115–125. | MR