Abstract
We construct two new series of closed left ideals of the semigroup\(\bar \tau \) of ultrafilters of a topological group (G, τ). The first series gives a disjunctive decomposition of τ-absorbing ultrafilters. Under certain restrictions on the topology of the group (G, τ), the second series gives a disjunctive decomposition of the semigroup of free ultrafilters. For a nondiscrete metrizable topological group (G, τ), we construct a large free subsemigroup of the semigroup\(\bar \tau \).
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References
I. V. Protasov, “Ultrafilters and topologies on groups,”Sib. Mat. Zh.,34, No. 5, 163–180 (1993).
N. Hindman, “Ultrafilters and combinatorial number theory,”Lect. Notes Math.,751, 49–184 (1979).
W. Ruppert, “In a left-topological semigroup with dense center the closure of any left ideal is an ideal,”Semigroup Forum,36, 247 (1987).
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 4, pp. 506–511, April, 1995.
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Protasov, I.V. Ideals of the semigroup of ultrafilters of a topological group. Ukr Math J 47, 588–593 (1995). https://doi.org/10.1007/BF01056044
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DOI: https://doi.org/10.1007/BF01056044