On a problem of Bertram Yood
Mart Abel ; Mati Abel
Topological Algebra and its Applications, Tome 2 (2014), / Harvested from The Polish Digital Mathematics Library
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In 1964, Bertram Yood posed the following problem: whether the intersection of all closed maximal regular left ideals of a topological ring coincides with the intersection of all closed maximal regular right ideals of this ring. It is proved that these two intersections coincide for advertive and simplicial topological rings and, using this result, it is shown that the topological left radical and the topological right radical for every advertive and simplicial topological algebra coincide.

Publié le : 2014-01-01
EUDML-ID : urn:eudml:doc:266765 
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     volume = {2},
     year = {2014},
     zbl = {1294.16034},
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Mart Abel; Mati Abel. On a problem of Bertram Yood. Topological Algebra and its Applications, Tome 2 (2014) . http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_taa-2014-0001/

[1] G. Aumann, Aufau von Mittelwerten mehrerer Argumente. II. (Analytische Mittelwerte), Math. Ann. 111:1 (1935), 713-730. | Zbl 0012.25205

[2] G. Aumann, Über Räume mit Mittelbildungen, Math. Ann. 119 (1944), 210-215. | Zbl 0060.40005

[3] G. Aumann, C. Carathéodory, Ein Satz über die konforme Abbildung mehrfach zusammenhängender ebener Gebiete, Math.Ann. 109 (1934), 756-763. | Zbl 60.0285.04

[4] T. Banakh, O. Gutik, M. Rajagopalan, On algebraic structures on scattered compacta, Topology Appl. 153:5-6 (2005), 710-723. | Zbl 1087.22003

[5] R. Bonnet, W. Kubis, Semilattices, unpublished note.

[6] B. Eckmann, Räume mit Mittelbildung, Comm. Math. Helv. 28 (1954), 329-340. | Zbl 0056.16403

[7] P. Hilton, A new look at means on topological spaces, Internat. J. Math. Math. Sci. 20:4 (1997), 617-620. [Crossref] | Zbl 0907.55010

[8] K. Hofmann, M. Mislove, A. Stralka, The Pontryagin duality of compact O-dimensional semilattices and its applications, Lecture Notes in Math., Vol. 396. Springer-Verlag, Berlin-New York, 1974. | Zbl 0281.06004

[9] I. Parovichenko, On a universal bicompactum of weight @, Dokl. Akad. Nauk SSSR, 150 (1963), 36-39.

[10] A. Teleiko, M. Zarichnyi, Categorical Topology of Compact Hausdor spaces, VNTL Publ., Lviv, 1999. | Zbl 1032.54004

[11] F. Trigos-Arrieta, M. Turzanski, On Aumann’s theorem that the circle does not admit a mean, Acta Univ. Carolin. Math. Phys. 46:2 (2005), 77-82.