On a problem of Bertram Yood

Mart Abel; Mati Abel

Topological Algebra and its Applications (2014)

  • Volume: 2, Issue: 1, page 1-4, electronic only
  • ISSN: 2299-3231

Abstract

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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.

How to cite

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Mart Abel, and Mati Abel. "On a problem of Bertram Yood." Topological Algebra and its Applications 2.1 (2014): 1-4, electronic only. <http://eudml.org/doc/266765>.

@article{MartAbel2014,
abstract = {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.},
author = {Mart Abel, Mati Abel},
journal = {Topological Algebra and its Applications},
keywords = {Topological ring; advertive topological ring; invertive topological ring; simplicial topological ring; Yood problem; topological algebra; topological radical of a topological algebra; closed maximal regular left ideals; advertive topological rings; simplicial topological rings; topological radicals; topologically quasi-invertible elements},
language = {eng},
number = {1},
pages = {1-4, electronic only},
title = {On a problem of Bertram Yood},
url = {http://eudml.org/doc/266765},
volume = {2},
year = {2014},
}

TY - JOUR
AU - Mart Abel
AU - Mati Abel
TI - On a problem of Bertram Yood
JO - Topological Algebra and its Applications
PY - 2014
VL - 2
IS - 1
SP - 1
EP - 4, electronic only
AB - 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.
LA - eng
KW - Topological ring; advertive topological ring; invertive topological ring; simplicial topological ring; Yood problem; topological algebra; topological radical of a topological algebra; closed maximal regular left ideals; advertive topological rings; simplicial topological rings; topological radicals; topologically quasi-invertible elements
UR - http://eudml.org/doc/266765
ER -

References

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  1. [1] G. Aumann, Aufau von Mittelwerten mehrerer Argumente. II. (Analytische Mittelwerte), Math. Ann. 111:1 (1935), 713-730. Zbl0012.25205
  2. [2] G. Aumann, Über Räume mit Mittelbildungen, Math. Ann. 119 (1944), 210-215. Zbl0060.40005
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  6. [6] B. Eckmann, Räume mit Mittelbildung, Comm. Math. Helv. 28 (1954), 329-340. Zbl0056.16403
  7. [7] P. Hilton, A new look at means on topological spaces, Internat. J. Math. Math. Sci. 20:4 (1997), 617-620. [Crossref] Zbl0907.55010
  8. [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. Zbl0281.06004
  9. [9] I. Parovichenko, On a universal bicompactum of weight @, Dokl. Akad. Nauk SSSR, 150 (1963), 36-39. 
  10. [10] A. Teleiko, M. Zarichnyi, Categorical Topology of Compact Hausdor spaces, VNTL Publ., Lviv, 1999. Zbl1032.54004
  11. [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. 

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