Geodesic
On the existence of a Haar measure in topological IP-loops
Kybernetika, Tome 47 (2011) no. 5, pp. 740-754 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

In this paper, we give conditions ensuring the existence of a Haar measure in topological IP-loops.
In this paper, we give conditions ensuring the existence of a Haar measure in topological IP-loops.
Classification : 20N05, 28C10
Keywords: quasigroup; topological IP-loop; Haar measure; content; uniform; space; left-invariant uniformity 
@article{KYB_2011_47_5_a6,
     author = {Stehl{\'\i}kov\'a, Be\'ata and Markechov\'a, Dagmar and Tirp\'akov\'a, Anna},
     title = {On the existence of a {Haar} measure in topological {IP-loops}},
     journal = {Kybernetika},
     pages = {740--754},
     year = {2011},
     volume = {47},
     number = {5},
     mrnumber = {2850461},
     zbl = {1242.28022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2011_47_5_a6/}
}
TY  - JOUR
AU  - Stehlíková, Beáta
AU  - Markechová, Dagmar
AU  - Tirpáková, Anna
TI  - On the existence of a Haar measure in topological IP-loops
JO  - Kybernetika
PY  - 2011
SP  - 740
EP  - 754
VL  - 47
IS  - 5
UR  - http://geodesic.mathdoc.fr/item/KYB_2011_47_5_a6/
LA  - en
ID  - KYB_2011_47_5_a6
ER  - 
%0 Journal Article
%A Stehlíková, Beáta
%A Markechová, Dagmar
%A Tirpáková, Anna
%T On the existence of a Haar measure in topological IP-loops
%J Kybernetika
%D 2011
%P 740-754
%V 47
%N 5
%U http://geodesic.mathdoc.fr/item/KYB_2011_47_5_a6/
%G en
%F KYB_2011_47_5_a6
Stehlíková, Beáta; Markechová, Dagmar; Tirpáková, Anna. On the existence of a Haar measure in topological IP-loops. Kybernetika, Tome 47 (2011) no. 5, pp. 740-754. http://geodesic.mathdoc.fr/item/KYB_2011_47_5_a6/

[1] Baez, J.: The Octonions. Bull. Amer. Math. Soc. 39 (2002), 145–205. | DOI | MR | Zbl

[2] Belousov, V. D.: Foundations of the Theory of Quasigroups and Loops (in Russian). Nauka, Moscow, 1967. | MR

[3] Bruck, R. H.: Some results in the theory of quasigroups. Trans. Amer. Math. Soc. 55 (1944), 19–52. | MR | Zbl

[4] Bruck, R. H.: Contributions to the theory of loops. Trans. Amer. Math. Soc. 60 (1946), 245–354. | MR | Zbl

[5] Haar, A.: Der Massbegriff in der Theorie der kontinuierlichen Gruppen. Ann. Math. 34 (1933), 147–169. | DOI | MR | Zbl

[6] Halmos, P.: Measure Theory. Springer-Verlag New York Inc. 1974. | MR | Zbl

[7] Hudson, S. N.: Transformation groups in the theory of topological loops. Proc. Amer. Math. Soc. 15 (1964), 872–877. | DOI | MR

[8] Hudson, S. N.: Topological loops with invariant uniformities. Trans. Amer. Math. Soc. 109 (1963), 1, 181–190. | DOI | MR | Zbl

[9] Chein, O., Pflugfelder, H. O., Smith, J. D. H.: Quasigroups and Loops. Theory and Application. Heldermann Verlag, 1990. | MR | Zbl

[10] Kinyon, M. K., Kunen, K., Phillips, J. D.: Every diassociative A-loop is Moufang. Proc. Amer. Math. Soc. 130 (2002), 619–624. | DOI | MR | Zbl

[11] Markechová, D., Stehlíková, B., Tirpáková, A.: The uniqueness of a left Haar measure in topological IP-loops. (Submitted for publication).

[12] Moufang, R.: Zur Struktur von alternativ Korpern. Math. Ann. 110 (1935), 416–430. | DOI | MR

[13] Nagy, P. T., Strambach, K.: Coverings of topological loops. J. Math. Sci. 137 (2006), 5, 5098–5116. | DOI | MR | Zbl

[14] Nagy, P. T., Strambach, K.: Loops in Group Theory and Lie Theory. De Gruyter Expositions in Mathematics, Berlin – New York 2002. | MR | Zbl

[15] Pflugfelder, H. O.: Quasigroups and Loops. Introduction. Heldermann Verlag, 1990. | MR | Zbl

[16] Riečan, B., Neubrunn, T.: Integral, Measure and Ordering. Kluwer Academic Publishers 1997. | MR

[17] Schwarz, Š.: On the existence of invariant measures on certain types of bicompact semigroups (in Russian). Czechoslovak Math. J. 7 (1957), 82, 165–182. | MR

[18] Smith, J. D. H.: Quasigroup Representation Theory. Taylor & Francis, 2006.

[19] Weil, A.: Basic Number Theory. Academic Press, 1971.