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Title: A cancellative amenable ascending union of nonamenable semigroups (English)
Author: Donnelly, John
Language: English
Journal: Czechoslovak Mathematical Journal
ISSN: 0011-4642 (print)
ISSN: 1572-9141 (online)
Volume: 61
Issue: 3
Year: 2011
Pages: 687-690
Summary lang: English
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Category: math
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Summary: We construct an example of a cancellative amenable semigroup which is the ascending union of semigroups, none of which are amenable. (English)
Keyword: amenability
Keyword: semigroups
Keyword: ascending union
MSC: 20M99
MSC: 43A07
MSC: 43A17
idZBL: Zbl 1249.43001
idMR: MR2853083
DOI: 10.1007/s10587-011-0039-5
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Date available: 2011-09-22T14:37:09Z
Last updated: 2020-07-03
Stable URL: http://hdl.handle.net/10338.dmlcz/141630
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Reference: [1] Banach, S.: Sur la problème de la mesure.Fundamenta math. 4 (1923), 7-33.
Reference: [2] Day, M. M.: Amenable semigroups.Ill. J. Math. 1 (1957), 509-544. Zbl 0078.29402, MR 0092128, 10.1215/ijm/1255380675
Reference: [3] Day, M. M.: Semigroups and amenability.(Semigroups, Proc. Sympos. Detroit, Michigan, 1968), pp. 5-53, Academic Press, New York (1969). Zbl 0191.01801, MR 0265502
Reference: [4] Donnelly, J.: An amenable ascending union of non-amenable semigroups.Int. J. Algebra Comput. 17 (2007), 179-185. Zbl 1126.20042, MR 2300412, 10.1142/S0218196707003524
Reference: [5] Følner, E.: On groups with full Banach mean value.Math. Scand. 3 (1955), 243-254. MR 0079220, 10.7146/math.scand.a-10442
Reference: [6] Frey, A. H.: Studies on Amenable Semigroups.PhD thesis, University of Washington (1960). MR 2613109
Reference: [7] Grigorchuk, R. I.: Growth and amenability of a semigroup and its group of quotients.Semigroup theory and its related fields, Proc. Int. Symp., Kyoto/Jap. (1990), 103-108. Zbl 0726.43002, MR 1099852
Reference: [8] Grigorchuk, R. I.: Invariant measures on homogeneous spaces.Ukr. Math. J. 31 (1980), 388-393. Zbl 0447.28010, MR 0552478, 10.1007/BF01126860
Reference: [9] Grigorchuk, R. I., Stepin, A. M.: On amenability of semigroups with cancellation.Mosc. Univ. Math. Bull. 53 (1998), 7-11. Zbl 1023.43001, MR 1708545
Reference: [10] Hausdorff, F.: Grundzüge der Mengenlehre.Leipzig (1914).
Reference: [11] Hochster, M.: Subsemigroups of amenable groups.Proc. Am. Math. Soc. 21 (1969), 363-364. Zbl 0174.30801, MR 0240223, 10.1090/S0002-9939-1969-0240223-0
Reference: [12] Klawe, M.: Semidirect product of semigroups in relation to amenability, cancellation properties, and strong Følner conditions.Pac. J. Math. 73 (1977), 91-106. Zbl 0385.43001, MR 0470609, 10.2140/pjm.1977.73.91
Reference: [13] Namioka, I.: Følner's conditions for amenable semi-groups.Math. Scand. 15 (1964), 18-28. Zbl 0138.38001, MR 0180832, 10.7146/math.scand.a-10723
Reference: [14] Neumann, J. Von: Zur allgemeinen Theorie des Masses.Fundamenta 13 (1929), 73-116.
Reference: [15] Olśhanskii, A. Yu.: On the problem of the existence of an invariant mean on a group.Russ. Math. Surv. 35 (1980), 180-181. MR 0586204, 10.1070/RM1980v035n04ABEH001876
Reference: [16] Sorenson, J.: Existence of Measures that are Invariant Under a Semigroup of Transformations.PhD thesis, Purdue University (1966). MR 2616074
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